Putting myself in your shoes, not be able to get the deer out and use the meat, I would've done exactly what you did, not shoot. I personally feel like I would feel worse for killing an animal and not being able to get it out of the woods or use the meat than I would for letting nature take its course. If there was no visible sign of injury, it could be an old one that she's been dealing with for a while, and if she had yearlings (fawns, or last year's offspring) with her, she might very well be coping with it just fine.
I think you did the right thing, and I would've done the same.