In the film's official novelisation Palpatine and Anakin agree not to tell the truth about what happened.
“And we won’t. Just as we need never speak of what has happened here today.” It was as though the shadow itself spoke kindly. “I have always kept your secrets, have I not?”
When asked what happened by Mace and the Jedi Council, Anakin demurs to the Chancellor who describes it as an epic lightsaber fight that ended with Anakin winning (e.g. killing Dooku).
“Count Dooku was there,” Skywalker interjected. He had a look on his face that Mace couldn’t decipher, proud yet wary— even unhappy. “He’s dead now.”
“Dead?” He looked from Anakin to Obi-Wan and back again. “Is this true? You killed Count Dooku?”
“My young friend is too modest; he killed Count Dooku.” Smiling, Kenobi touched the lump on his head. “I was … taking a nap.”
“But …” Mace blinked. Dooku was to the Separatists what Palpatine was to the Republic: the center of gravity binding together a spiral galaxy of special interests. With Dooku gone, the Confederacy of Independent Systems would no longer really be a confederacy at all. They’d fly to pieces within weeks.
Mace said again, “But …”
And, in the end, he couldn’t think of a but.
This was all so astonishing that he very nearly-almost, but not quite-cracked a smile.
“That is,” he said, “the best news I’ve heard since …” He shook his head. “Since I can’t remember. Anakin-how did you do it?”
Inexplicably, young Skywalker looked distinctly uncomfortable; that newly confident presence of his collapsed as suddenly as an overloaded deflector, and instead of meeting Mace’s eyes, his gaze flicked to Palpatine. Somehow Mace didn’t think this was modesty. He looked to the Chancellor as well, his elation sinking, becoming puzzlement tinged with suspicion.
“It was … entirely extraordinary,” Palpatine said blandly, oblivious to Mace’s narrowing stare. “I know next to nothing of swordplay, of course; to my amateur’s eye, it seemed that Count Dooku may have been … a trace overconfident. Especially after having disposed of Master Kenobi so neatly.”
Obi-Wan flushed, just a bit-and Anakin flushed considerably more deeply.
“Perhaps young Anakin was simply more … highly motivated,” Palpatine said, turning a fond smile upon him. “After all, Dooku was fighting only to slay an enemy; Anakin was fighting to save-if I may presume the honor-a friend.”
Anakin is then pressed by Mace to provide "a full report", but there's no reason to assume he didn't tell the same story; he and Obi-Wan engaged Dooku, Dooku knocked Obi-Wan unconscious, they fought and the fight ended with Dooku's death.