Are you sure it wasn't hit? I've never heard of a deer stumbling from the sound of a shot. I've seen deer go a long way before starting to bleed out. Most of the time this happens if you hit the chest cavity a bit high as the blood has to fight gravity to bleed out.
If you did miss the deer I'd recomend a bit of practice. Mussle memory will help carry you through when your mind goes nuts in excitement. Even shooting a BB gun in the offseason will help give you practice. I do it myself. I print out a 1/10th size deer target that I pin to scrap sheets of drywall. Visually at 10 yards it compares pretty well to a real deer at 100 yards.