Palpatine knew that he didn't kill Yoda, from knowing and seeing what had happened.
From Mathhew Stover's "Revenge of the Sith" novelization:
The base of the Arena was a hundred meters below, littered with twisted scraps and jags of metal from the pods destroyed in the battle, and as the little green freak fell, finally, above, the victorious shadow became once again only Palpatine: a very old, very tired man, gasping for air as he leaned on the pod’s rail.
Old he might have been, but there was nothing wrong with his eyesight; he scanned the wreckage below, and he did not see a body.
He flicked a finger, ... Clone troops were already swarming into it.
“It was Yoda,” he said as he swung out of the pod. “Another assassination attempt. Find him and kill him. If you have to, blow up the building.”