The worst part for Order 66, though, was that it wasn't simultaneous. Sidious took sadistic glee in not issuing the order all at the same time to the clone commanders, but contacted them all one by one to personally order the Jedi's executions. This meant that quite a few Jedi could sense their brethren all across the galaxy dying one after another...except they couldn't see how it was happening or who was behind them. The Shroud of the Dark Side and all the death and suffering caused by the Clone Wars had completely blinded* their precognitive abilities by then, and not sensing any ill intent from the clones around them, they were literally running around in circles blind to the danger.
*Yoda only managed to pierce the Shroud of the Dark Side while fighting Darth Sidious at the Senate, and even then it's possible he only managed to pierce it because he was starting to slip into the Dark Side. Watch the scene again in the movie, as Sidious pours Force Lightning at Yoda, who's beginning to get forced back, before suddenly looking angrily at Sidious at which point he starts forcing him back.
Just like Kreia pierced the First Child's sorcery thanks to being Sith herself, allowing her to perceive the True Sith's existence, Yoda's brief touch of the Dark Side allowed him to pierce the Order of Bane's sorcery. It even adds more meaning to his statement to Bail, "Failed, I have..."
He didn't just mean he failed to defeat Darth Sidious, he also failed as a Jedi, as he couldn't match the Dark Lord's power without tapping ever so little into the Dark's power.