Man, doesn't make any difference if it's a cat, a dog, or a gerbil. It's just damn hard to make that decision to have a beloved pet/companion/friend put down - there's a reason it's called "having your pet put to sleep" you know - because it makes it a little easier, so they think, for us confronted with such a decision to think yeah, that's right, we're just having Jocques/Tasha put to sleep, this isn't about death. Oh, how we love to fool ourselves, but we know what's really going on. Shit yeah, it's hard, but you did the right thing. As hard as it was to take my first Jocques and then a few years later Tasha, into the vet to have the deed done, I know it was the right thing. I think every pet owner knows when that time comes - some just don't want to face it. You were very brave to do so, and you saved your loved one undue pain and suffering. They can't talk to us like humans can, and we still are not sure how much pain they suffer, how much agony they endure, before they just can't get up out of their beds anymore. I sometimes wonder if I waited too long, and I feel guilty about that - about causing my beloved companions more pain and suffering because I was too selfish and cowardly to let them go.
I've come to the conclusion that we are more HUMANE to our pets than we are in our treatment of ourselves.
You did the right thing. Don't second guess yourself and don't be "guilted" into feeling other than that you DID do the right thing. You had the guts to do what is right.