Magnolia, so sorry for your loss.
I've had to put down several of my beloved fur companions. I've done it before I got sober and got drunk as a way to handle it. I've done it while sober. Drinking didn't bring my dog back. Being drunk really didn't make me grieve their loss any less.
It's just as hard saying goodbye to a pet sober. The difference was, I wasn't miserable and shameful about my drinking. I've learned it is okay to be sad and grieve for a pet. I don't need alcohol to handle it.
Be the sober, human companion your dog loved.