Mike,
Take heart. This reminds me of a situation a few years ago when I was hunting one morning when a mature doe came in. She was at a slow walk when I mouth grunted to get her to stop (I never will do that again). She stopped at full alert at 18yds when I pick a spot, drew and released. At the shot she started to drop! Not her first rodeo and the Woodsman hit her square in the shoulder blade. A very loud SMACK and she tore out like she was running from the he?? hounds. I was mortified as yourself and could not believe what happened. I could hear the arrow bouncing off brush and trees as she ran. I got down to check for blood hoping I got enough penetration as most of the arrow was still sticking out and to see what blood was on the ground. I found the arrow without the broadhead about 65 yds. from the shot and when I bent down to pick it up she took off. She was standing, watching me about 50yds away and bounded away with her tail up. I never found her.
Three years later one of my brothers was hunting the property during the muzzloader season and shot a mature doe. Upon butchering he found my Woodsman broadhead buried in the scapula with about 1/4 to 3/8" of the tip coming through. Not enough to get the job done. I'm betting the deer you shot will be fine and if one hunts long enough this situation is going to happen.
Chin up and get back at it!
Dave Brent