TL;DR: Tarkin is fully aware that there were Jedi - he fought alongside them in the Clone Wars. But the Empire was desperate to erase the Jedi from the galaxy's collective memory, and invested a tremendous amount of time and energy into making this happen. It was largely effective.
Note: Italics in all quotes is from the original; bold is mine.
Problems with the question:
Tarkin never says or does anything that would suggest he doesn't believe in the Force, or doesn't know about the Jedi.
The Jedi are extinct, their fire has gone out of the universe. You, my friend, are all that's left of their religion.
Here, he is simply saying "Vader, the Jedi are all dead, and you're the only person who uses the Force". This is true, as far as he knows - and he knows what he knows because he helped exterminate the Jedi. And he's not far off from the truth - when he delivers this line, there are only two Jedi (Obi-Wan and Yoda) left in a galaxy inhabited by quadrillions of people - and he doesn't know that either of those Jedi are still alive, because they've both been in hiding for 20 years.
And Motti isn't quite saying "The Jedi are a myth, and the Force doesn't exist".
Don't try to frighten us with your sorcerer's ways, Lord Vader. Your sad devotion to that ancient religion has not helped you conjure up the stolen data tapes, or given you clairvoyance enough to find the rebels' hidden fortress...
He's basically saying "The Jedi don't exist any more, and the Force is stupid. The Death Star is way better than whatever you can do with the Force."
The galaxy as a whole, and the Imperial rank-and-file:
In the Disney Canon novel Star Wars: Lost Stars, two Imperial cadets, the top of their class in the most prestigious Imperial Academy in the galaxy, know little or nothing about the Jedi, despite the fact that Order 66 was only enacted about 10 years earlier:
Yet the Imperial Palace was one of the grandest and most elegant structures on the entire planet; apparently it had once been a temple of some kind.
- Star Wars: Lost Stars
The "temple of some kind" the character is describing, now the Imperial palace, is the former Jedi Temple on Coruscant. It had been a Jedi Temple for thousands of years, until only 10 years earlier.
Even earlier, just a few years after Order 66, the galaxy had already ceased to believe in the Force, and the Jedi seemed like nothing more than a myth:
So far as Ciena could tell from the few holos she’d ever been able to watch, most people in the galaxy no longer believed in the Force, the energy that allowed people to become one with the universe. Even she sometimes wondered whether there could ever have been such a thing as a Jedi Knight. The amazing tales the elders told of valiant heroes with lightsabers, who could bend minds, levitate objects— surely those were only stories.
Later, the other student - who has since become an officer, then abandoned the Empire after witnessing the destruction of Alderaan - joins the Rebellion, but still regards Jedi and the Force as silly superstitions. This is remarkable, considering the fact that he's talking to Dak, who actually knows Luke:
It was all Thane could do not to groan. Please, not more superstitious nonsense about the “Force.” In his opinion, the rebel troops needed to be motivated by the harsh truth about the Empire, not crazy religious beliefs.
So the Empire's attempt to conceal the fact that the Jedi had ever existed was extremely successful, and that success came very quickly.
Grand Moff Tarkin:
As for Tarkin himself, we can turn to the Disney Canon novel Star Wars: Tarkin. Tarkin fought under and alongside Jedi - including Anakin Skywalker and Obi-Wan Kenobi - during the Clone Wars. He knows their history. He suspects that Vader and Palpatine are Sith. And he even knows - or is nearly certain - that Anakin became Vader.
Tarkin realized that the Emperor’s current residence had once been the headquarters for the Jedi — though practically all that remained of the Order’s elegant Temple complex was its copse of five skyscraping spires, now the pinnacle of a sprawling amalgam of blockish edifaces with sloping façades.
- Star Wars: Tarkin
Not only does Tarkin know that the Jedi existed - he also suspects that Vader and the Emperor are Sith, and wonders if Palpatine lied about the circumstances under which his face was deformed and Mace Windu (and three other Jedi Masters) died:
There were many stories about what had occurred that day in the chancellor’s office. The official explanation was that members of the Jedi Order had turned up to arrest Supreme Chancellor Palpatine, and a ferocious duel had ensued. The matter of precisely how the Jedi had been killed or the Emperor’s face deformed had never been settled to everyone’s satisfaction, and so Tarkin had his private thoughts about the Emperor, as well. That he and Vader were kindred spirits suggested that both of them might be Sith. Tarkin often wondered if that wasn’t the actual reason Palpatine had been targeted for arrest or assassination by the Jedi.
Even to Tarkin - who knew many Jedi - the Jedi seem to be a myth, only 5 years after Order 66; he also begins to work out who Vader really is:
That look again, Tarkin thought — or at least that suggestion of a look that always made him feel as if Vader knew him from some previous life.
“We no longer speak of the Jedi,” Mas Amedda had said when they had watched Vader issue his warnings to members of Coruscant’s underworld. It struck Tarkin now that the Chagrian’s attitude wasn’t one that was confined to the Emperor’s court. In the five short years since the Order had been eradicated— Jedi Masters, Jedi Knights, and Jedi Padawans wiped out by the very clone troopers they had commanded and fought beside— the Jedi already seemed a distant memory.
The depth of his knowledge of the Jedi is also revealed:
Tarkin had respected the Jedi as peacekeepers, but as generals they had proven failures. The Jedi Master with whom he had served most closely during the Clone Wars was Even Piell, to whom Tarkin’s cruiser had been assigned. Brusque and bellicose, the Lannik excelled in lightsaber combat, seeming to have integrated every possible fighting style, but he, too, had his flaws as a strategist. If Piell had deferred to Tarkin during their mission to investigate a hyperlane shortcut into Separatist-held space, they might have avoided capture and imprisonment, and perhaps the Lannik would have survived at least until the end of the war.
The Force had endowed the Jedi with wondrous powers, but their biggest failing was in not having used the Force in all ways possible to bring the war to a quick end. By remaining faithful to their ethical code, they had allowed the war to drag on and spiral downward into a meaningless bloodbath. The conflict’s sudden conclusion and the Order’s decision to depose Supreme Chancellor Palpatine. had taken nearly everyone by surprise. But Tarkin suspected that even if the Jedi had restrained themselves from rising against Palpatine in his moment of glory, the esoteric Order had doomed itself to extinction. Where their flame had burned bright for a thousand generations, technological might was the new standard.
Tarkin was already well aware of Vader's affinity for Force-choking people, more than a decade before the incident aboard the Death Star:
Tarkin knew merely by the gasping sounds that began to erupt from the Sugi that Vader was performing that thumb-and-forefinger dark magic of his to crush the crime lord’s windpipe.
And ultimately, he figured out - though he wasn't quite sure - who Vader really was:
Tarkin didn’t always agree with Vader’s methods for dealing with those who opposed the Empire, but he held the Dark Lord in high esteem, and he hoped Vader felt the same toward him. Very early on in their partnership — soon after both had been introduced to the secret mobile battle station — Tarkin grew convinced that Vader knew him much better than he let on, and that behind the bulging lenses of his face mask, whatever remained of Vader’s human eyes regarded him with clear recognition. More than anything else it was those initial feelings that had provided Tarkin with his first suspicion as to Vader’s identity. Later, observing the rapport the Dark Lord shared with the stormtroopers who supported him, and the technique he displayed in wielding his crimson lightsaber, Tarkin grew more and more convinced that his suspicions were right.
Vader might very well be Jedi Knight Anakin Skywalker, whom Tarkin had fought beside during the Clone Wars, and for whom he had developed a grudging appreciation.
The Emperor was aware of Tarkin's suspicions, but didn't see them as a problem, because Tarkin clearly didn't mind being led by two Sith:
Sidious assumed that Tarkin had puzzled out that Vader had once been Anakin Skywalker, under whom Tarkin had served during the war. Tarkin may also have determined that Vader was a Sith. If so, it followed that he accepted that Sidious was Vader’s dark side Master. But Tarkin’s intuitions were important only in the sense that he never revealed them and never allowed them to interfere with his own ambitions.
The Emperor had long sought to foster a friendship between Anakin and Tarkin, but it didn't work until after Anakin became Vader:
During the Clone Wars, Sidious had made every attempt to promote a rapport between Skywalker and Tarkin, but the relationship had never prospered to his satisfaction. Then came that business with Skywalker’s Togruta apprentice, Ahsoka Tano, which, while it had provoked further disaffection in Skywalker, had also created a rift between him and Tarkin that perhaps had yet to mend. Yes, they had partnered since the end of the war, but— to Sidious’s own annoyance— absent a true appreciation for each other’s talents.
Why Palpatine tried to cover up the existence of the Jedi:
Because as long as people believed in the Force, and knew the true value of the Jedi, the Force might exert itself and restore balance - by destroying Palpatine, the Empire, and the Sith:
Darth Plagueis had once remarked that “the Force can strike back.” The death of a star didn’t necessarily curtail its light, and indeed Sidious could see evidence of that sometimes even in Vader — the barest flicker of persistent light. Attacks like the one directed against Tarkin’s moon base [where the Death Star was under construction] and discoveries like the one on Murkhana were distractions to his ultimate goal of making certain that the Force could not strike back, and that whatever faint light of hope remained could be snuffed out for good.