Lets start with the assumption that a guy practices and can hit what he wants to hit with consistency.  Then a miss is an anomaly and you need a short memory.  Shoot a few practice arrows to confirm the fact that you can hit your target and get back in the hunt.
Joe

Missing a shot is like swinging and missing a baseball. You get back in the box and prepare for the next pitch.

Same with bowhunting...miss...grab another arrow and hope the animal gives you a second chance. Don't think about it, dwell on it or whatever. You know your shooting abilities, why put negative thoughts in your head.

Assessment first, then a pipe and scotch while devising a remedy.

1) Did the animal jump the string? If not, what did I do wrong? I have total confidence that when I hit my anchors, pick a spot, and expand through the shot, the arrow will go where I look. A few possible errors to correct makes the mind focus on a few simple remedies, instead of panicking.

2) Smoke and beverages help the mind relax, keeping me from blowing the miss out of proportion, which could turn it into a nasty gremlin for a long time. I prefer English blends out of a custom pipe my brother gifted to me. (not to mention that he happens to be the maker). A glass of Ardbeg finishes the healing process nicely.
 

I like Malachi's methoud....  

I just grab the next arrow in my quiver

I shoot a blunt at an object about the same distance as my miss. If it hits where it is suppose to, I keep on hunting with a lip pooch. If it does not hit where it is suppose to, a quiver emptying might be in the making.