It really hurts when you lose an animal, especially when you have to watch them get put down. I know how it feels.
You'll start to feel the stages of grievance becoming more thresholding by later today and so on, but it goes away. It helps to understand that regardless of how hurtfull and guilty you feel, you put the dog out of it's suffering, and you did the right thing.
Animal's are companions, they are to be loved and when their time comes, then it's their time, and if you need to put them down from something such as disease or suffering, it's better than letting them suffer and die.