It's true that bow wounded deer do not suffer and die painful lengthy deaths as animal rights activists would have you believe. A thesis study performed by Wendy Krueger and the Minnesota DNR several years ago at Camp Ripley showed conclusively that bowmen recover their wounded animals or those not found, recover. The wound-loss ratio was calculated at something less than 10%. Further independent studies show that arrow wounded deer that are not recovered typically recover from their wounds, especially when those wounds entered a non-vital area, including the gut.
My advice to first time bowhunters is to never take any shot that isn't absolutely perfect. That is, the animal is relaxed, head turned away, with a broadside or slightly quartering away position offered. In addition, keep even those shots less than 20 yards. Most folks who can drill paper or 3-D targets on a range can't always shoot as accurately on live game. Therefore, you have to reduce the chances of mistakes by taking your time.
I always carry two field pointed arrows in my quiver and take practice shots at unknown distances from my treestands. During squirrel season I even shoot squirrels during this practice. Once, after shooting a squirrel, a red fox ran up and grabbed the squirrel off of my arrow (stuck in the ground), breaking the arrow. I quickly nocked a broadhead and bagged the red fox. Both shots were within 11 yards.
Deer are incredibly resilient to injuries. Deer jumping fences often do flips landing on their heads or backs, or are even stabbed by branches or fence posts during their fall. Younger bucks are always being stabbed by older dominant bucks with larger antlers. In populated areas, you'd be surprised at just how many deer survive incredible deer/vehicle collisions.
But back to deer recovery...it sounds like your arrow didn't make it through both lungs if at all. The fact that your arrow did not make a complete pass through is indicative of a marginal shot, since full bellies can stop an arrow from doing any damage to vitals (which are located much further forward than you say your arrow entered). At the end of your blood trail (which you should mark with toilet paper to see a traveling pattern), start making ever widening circles away from your last blood trail. Marginally hit animals will usually get back onto game trails, so look on those as well. A mortally hit animal (with an arrow wound) will typically be dead within 100 yards from where you originally hit it. Marginal shots, hitting only one lung can allow for hundreds of yards of travel. You owe it to the animal to keep searching, even if to finally conclude that your deer did not die.
As in any endeavor, we learn from our mistakes. Evaluate your hunt that day, and correct what needs correcting. Practice, practice, practice. Keep your shots short with archery equipment, you'll feel alot more confident.