First of all, the obvious theory is that his Spider-sense was overflowing him with warning signals, because of the imminent mortal danger, but as opposed to the usual cases, there was absolutely nothing he could do, consciously or instinctively, to dodge or stop that danger.
Furthermore, Most characters seemed to go painlessly, sometimes without suspectign anything was wrong until they were gone, as you can see in Bucky, who saw his arm disappearing, casually told Steve, and was gone. T'Challa is trying to help a companion get up, and is completely unaware of his own death.
The characters who seem to know it's coming before literally seeing parts of them gone are Spider-man, Groot, Mantis and Strange. All of them can be explained.
Dr Strange probably saw it happening and expected to disappear with the rest, maybe with precise timing.
Mantis has some sort of connexion with feelings and emotions, and might have felt trillions disappearing. While this doesn't explain her own disappearance, she hasn't said anything suggesting she was aware of her own death, as opposed to aware of some deaths.
Groot fell down, and even said "Dad" before disappearing. Groot has a Healing factor, just like Spider-Man.
Maybe the disappearance gets rid of nerves at the same time as the rest, which is why nobody feels any pain. Given how important nerves are for avoiding danger, they might regenerate very fast, as some sort of priority, for characters with a Healing factor. This might be why Groot and Spider-man seemed to be in pain. Their Healing factor was trying to regenrate their nerves (with the rest), but couldn't keep up. Alternatively, the Healing factor itself "notived" it had to regenerate things, and this created a subconscious feeling of pain or fear, that was not present in people like Bucky or Sam.
Last but not least, of all the people we saw die, Spider-man was probably the youngest. Imagine a teenager who suddenly finds himself superpowers, and probably felt some "I'm invincible adrenaline" in addition to hormones and extreme stress, suddenly realizing he is dying and can't do anything to prevent it. Peter is Desesperate, panicking, and extremely scared. Of course his reaction is perfectly realistic in that situation. The other times he's been in danger, especially in Homecoming, Tony always had a trick to save him and fix things. His first instinct is to cry out to Tony to save him (he even says "Please Mr Stark"). He desesperately wants to be saved, like that time with the parachute or on the ferry, but deep down he knows there's nothing this time.
tl;dr: Peter knew it was coming due to spider-sense, was probably in pain due to his healing factor, and was already way over his head in a horrible and dangerous situation since several hours ago, so was extremely stressed. His reaction is to be expected.