I know how you feel; but I can tell you that if you shot OVER the spine - the deer is most likely to survive.
I had a pass through on a muledeer doe this fall; that I followed for miles. It eventually bedded; and after a stalk; it got up and ran off like nothing had happened to it. I found NO blood in the bed; although I followed a spot here and there to it; and I could see the deer until it bedded. It was hit over the spine - I could see the wound until the bleeding slowed: but thought it was a perfect shot when I made it.
I followed it for hours after that; and it eventually ran up a mountain and started feeding. I am sure it recovered.
Remember when deer are fighting; the antlers poke holes in them all the time ( one study of deer skins turned into tanneries showed over 70 heeled wounds per skin). Deer run into branches; and fences; and as I mentioned - other bucks- and recover.
There is a thread here somewhere that shows the organs of the deer; and such; I will look it up and add it here.
Certainly we do not shoot to just injure deer; we shoot to kill them; but remember; they are strong animals; and can recover from cuts--- which is what a broadhead does. Bullets kill by the damage from the bullet itself; but more from hydrostatic shock; the vibrations of the bullet.
Bullet wounds are hard to heal from; but arrow wounds are pretty easy for a deer to recover from.
Remember too- except for spine shots; we shoot and wound animals; and then they die from the wounds. It may take the animal a few steps to pass out from oxygen not reaching the brain; or it might take a couple hundred yards.
I can tell you as a very experienced bowhunter; with lots of kills with a bow; that the best way to lose a bow shot deer; is to have help finding the deer. As much as people mean well; they can miss obvious signs; or not so obvious signs; and step on sign- eliminating it.
I have seen deer run in circles; and drop right where I shot them; I have seen them run off; breed a doe; and fall over dead. I have tracked many deer for myself and others; and believe me; deer will do things that will confound you; and a slow steady 'keep to the blood trail' approach is really the best way to go; short of a good tracking dog.
I hit a buck through the heart once that ran 180 yards - yet died about 30 yards from where it was when I hit it. I had 'help' with that tracking job; and when they gave up; I started from the place the deer was shot; and in time; found the deer.
While misses and bad hits are reasons to practice more; and really try to be steady on the shot; and to pick a spot... its no reason to stop bowhunting. Rifle hunters in studies have proven they wound more deer than bowhunters do.
Again; its not our intent to lose deer. It happens; we try to not have it happen; but it can to anyone.
Did the arrow pass through the deer? Did you find the arrow; find a blood trail? What did the blood trail look like?
If you shot over the spine; the deer will most probably recover. I think you shot over - not under the spine.
Take an honest look at the deer in the thread; and tell me if you still think you shot under the spine.
Make your next arrow count