Did I do the right thing?

Hello Dr. Marie,
I am grieving today as I had my 12 year old cat put down yesterday and I am second guessing myself on the decision I made. A couple of nights ago my cat woke me at 4am crying pitifully at the bottom of the stairs. She had apparently fell down the stairs and had wiped out her food and water tray. She had also apparently defecated on the carpet up stairs and vomited before falling. She could not stand but was trying. I carefully picked her up and laid her down in the living room floor. She would try to stand but would just flop over. She would only lay on her left side. I took her to the vet. No injuries were found. Reflexes normal. Pupils responsive although she seemed to have difficulty focusing. She would try to raise her head and look around but could not maintain this but a few seconds. The Vet said it could be a brain lesion or possibly Vestibular Syndrome. I later learned the difference between central and peripheral vestibular syndrome. It seemed she fit the Central form though I cannot be sure. The vet gave her a anti nausea shot. After 24 hours she still could not move off her left side. She would not eat drink, or urinate. She also was drooling. I took her back to the Vet who offered to express her bladder and give an IV but indicated the odds were that she would not recover. So I opted to have her put down which the Vet said was not a "wrong" decision. She was an older cat and I felt she was suffering. I keep thinking maybe she could have pulled through. But I know now it's too late. Still I feel terrible. If you have any comments it will be appreciated. It has been therapeutic just to write this. Thank you.