I too have had to suffer with the putting down of three wonderful cats over the last several years. I felt sadness, but also profound relief that their suffering was over. I felt their everlasting love until the day they were put down. They did not seem to feel any pain, just went peacefully to sleep.
I know it is in some ways almost worse to lose a beloved pet than a human relative. Their sweetness and unconditional love makes them so precious!
At least now they are at rest and pain free. Don't be surprised if you hear a familiar meow in the middle of the night or feel a gentle rubbing against your leg. Love never dies!