How do you apologize to a cat?

Yesterday, I accidentally stepped on my cat's tail while trying to carry in groceries. It all happened so fast one second he was weaving around my legs like he always does, the next he let out the saddest yowl I’ve ever heard.

I immediately dropped everything and knelt, but he had already darted under the couch. I’ve had him for a few months now, and we’ve built a gentle, sweet bond. But today? He wouldn’t even look at me. I tried all his favourite things, his snacky treats, that crunchy toy mouse he’s obsessed with, even the soft pats on his chin, but he just flicked his tail and walked away.

I feel awful. I know he’ll probably come around when he’s ready (cats don’t do forgiveness on our schedule), but I’m curious how do you say sorry to a cat in a way they will understand? Is there something more I should do, or do I just give him space and hope he knows I’d never hurt him on purpose?