It's a terrible situation and I feel for you, but don't regret your decision. The alternative is much worse..
Our dog who I had grown up with since I was a small child was getting old. He was a big one, over 100 pounds. Walking him use to be easy but eventually his rear legs went out and he couldn't even drag himself by his two front legs because he was so old and tired.
He cried at night because his back hurt. I had to pick him up and carry him to the end of the block (never peed too close to the house, gotta have a large perimeter you know!) and held him as he peed. My sister even built a giant wooden contraption on wheels to try and let him move around with his two front legs.
None of that really worked. He still hurt, he cried a lot, he was embarrassed.
Eventually his whole body locked up. He couldn't even move his head. He was constantly trembling and whining. He hadn't eaten all day so i figured he was hungry, but since he couldn't lift his head or really chew I spoon fed him some milk and tiny bits of meat with a spoon.
It wasn't really working, and it was terrible for him and us to witness.
We had to take him to an emergency animal hospital on the other side of town and get him euthanized in the middle of the night. As he lay on that elevated bed thing on his favorite blanket I stared him right in the eyes and saw him staring at me as they stuck the needle in him.
Of course it was really, really fucking sad and terrible. But considering what he would have lived with otherwise, it was certainly the merciful thing.
OP it feels bad to "kill" your pet like that, but honestly the alternative is so much worse. That you were there for your cat at all is the best thing you could have done for it.
This world is a really cold dark and unfair place where everyone dies. The fact that we live such comfortable lives nowadays is frankly a cosmological farce. Sometimes we are reminded that though sometimes we're comfortable, the reality is we have to face death like this eventually - but that you were there for your cat is the best thing you could have done. Sorry.