I'm so sorry! But like the others said, there was nothing you could have done, and you even took the cat to the Vet, what a sweet and caring thing to do!
I can somewhat relate, I hit a rabbit once. It's a horrible feeling. I'm sure it was even worse for you, seeing how that cat might have had a family it belonged to, mine was "just" a wild rabbit.

I'm glad you're feeling a little better today.