Will I ever get over the death of my dog?

Yesterday I had to have my 13 year old dog put to sleep and I'm so upset. Now I'm wondering if I did the right thing. He had a prolapsed disc and could only hobble around on three legs and sometimes he would just collapse completely. He had surgery for the same problem six years ago and recovered well but when we took him to the vets this time she gave him a blood test and it showed he had a big problem with his liver and so given his age and the fact that he couldn't stand being away from us in the hospital we were advised against surgery again. I feel awful about having him put to sleep, his mind was still strong but his body was weak. Did I do the right thing?