The spirits of our fallen brothers will sleep soundly tonight...
"When the Death Star was destroyed, about half of the 501st Legion was still in the hanger getting into their ships. Of those who made it out, another third were caught in the explosion. I'd fought with some of those men for over twenty years. Afterwards, those of us that survived hooked up with a nearby Imperial fleet making a retaliatory strike on the Rebel's base on Yavin IV. It wasn't the best thought out plan, but we were cut off from our leaders, tired, and operating on instinct. If it wasn't for our training, we probably wouldn't have gotten past their orbital defenses."
"And so the battle over Yavin came to an end. I'm told we destroyed hundreds of Rebel ships that day. Even if it had been thousands, it wouldn't have made up for the Death Star."
In the end of the mission in Felucia, the clone narrator said that Aayla Sacura was one of few people that respect them, and he says that he hoped she had a swift death during Order 66.
The 501's relation to Order 66 in general. They know its coming, they know Aayla and hundreds of other innocent Jedi are going to die, and for all they know, they'll be the ones who end up killing them. And the narrator's words after the Felucia mission makes it clear that they hate themselves for what is to come...
From the perspective of the clones on Kamino (after the Empire has risen), the fact that they tried their hardest to stop the Empire ravaging their home, and it's still not enough. The expanded tale to that is even worse, as Boba murders the Prime Minister for it and the Anti-Clones are executed on the platforms.