I completely understand what you are feeling. My wife and I made the decision yesterday and today at 4:13pm, we sent our 15-1/2 yr old Golden Retriever across the Rainbow Bridge. We felt terrible at the Vet's office. My wife cried that we tricked our girl into going to the Vet, because she didn't know she wasn't coming home with us. It's really hitting now that we are home. I kept looking at the floor next to the table while we were eating. The same spot were just this afternoon she was laying and I was giving her bits of my PB&J sandwich.
As DaSDGuy said, it's a gut punch. It hurts, but deep down we know we made the right decision. You will make the right decision too.