You did right. Never let an animal suffer.
I'll relate what I saw last weekend too.
Last weekend was opening deer season here in Kentucky. My buddy shot a decent 10 pointer and as we dropped it off to get processed, I noticed a doe that had been head shot. Not my preferred kill method but hey, quick and painless, so I thought.
The boys working there pulled the doe up on a chain pull and got the skin off her. At that point, everyone was shocked to see that the doe had been shot at least 4 times in the top rear quarter. The shooter was in a tree stand and it looked like he shot right above her. Her rear end was tore up with bullet holes. She had also been shot once in the ribs. Finally, as mentioned, she was shot in the head.
As I looked at this doe, I guessed she was shot once in spine and dropped. As she tried to crawl away, they put 3 more rounds in her rear quarter without bothering to get out of the stand. Those didn't kill her, so the hunter got out of the stand and shot her once through the ribs. The shot was too far back for a lung shot, so it didn't do the job. Finally, they got around to killing her with a head shot.
Too me, if you can't do the right thing while hunting, you shouldn't be hunting.
Again, you did the right thing. I wish every hunter out there did too.