I feel so guilty about putting my dog to sleep, is this normal?

My dog was a 16 year old American Eskimo and he was deaf and not walking great (walking sideways, bumping into things). He could not hold his bladder and was going to the bathroom in the house the last few months, but I just picked up after him. On Tuesday, he could not walk at all, his back legs would give out. He was going to the bathroom on himself and I would have to clean up after him. On Wed. I brought him to the vet and the vet said he is old and he could do x-rays and give medication for him but it would be a long process and he would never walk great again, and basically telling me I would be a nurse to him. I chose to put him down and now I feel so terribly guilty and sad. I keep apologizing over and over in my head to him. I stayed with him and held him and I cannot get the image of him dying and heart stopping out of my head. He had such a strong heart, how could I stop it? He loved me and I loved him so much and I just chose to put him down instead of maybe trying harder to help him out. He loves being around me all of the time that I cannot imagine him wanting to leave. The vet said he was uncomfortable, but was he in pain? I just keep questioning if I did the right thing, I want him back :(