Its a tough situation, but a learning and humbling experience that most bowhunters eventually deal with. You did everything right, try to feel good about that. You just do not know, its even likely that the hit was not that lethal, and it will survive. Arrow wounds are quite clean, and deer often recover quickly from a marginal hit. I'd guess that with a quartering away deer, you hit a little too far forward, hitting shoulder, and or brisket. Either way, a deer can survive this shot as long as the pleural membrane was not significantly puntured, causing decompression of the lung(s). On a quartering away deer, my target is usally the last rib back. If you think about the sight picture you had, you might recall subconciously centering on the hollow spot behind the front shoulder. This is because even with a 3d target, most of us practice with the target broadside. If the deer's leg was extended forward - and you subconcoisly aimed there, I can almost assure you, you hit brisket, not the lung cavity.
Of course I'm making assumptions. But, from so many I've talked with, and my own "bad" experience, I think at the "moment of truth", sometimes our practice sessions, take over.
As far as watching the arrow flight, you need to practice this too. Form is important, but you really need to confirm your shot placement in the feild. Some folks I know dip the ends of their arrows in white, to help them follow its path. Myself, I like a gaudy fletching, and a flourescent nock. Confirming arrow placement and mentally marking the deer's tavel with landmarks, are probably 2 of the most important considerations in recovering a deer, in my mind.
Good luck in you future, I'm sure you will do fine.