A play on "Shoot your shot" when asking someone out, to "shat your shot" means you asked the person out, but you botched it with the result that you were rejected.
You "shat your shot" when you botch a proposal to ask someone on a date. For example, saying the wrong name.
:::Asking out Becky:::
"Hi! I was wondering if you wanted to go to the movies, Cindy."
You just shat your shot.
1) advanced 1337 slang phrase for "pwnd" or "prawnd"
2) the act of entering a state of being covered in human excrement
3) internet phrase to express utter humiliation during an online game
other variations include: having become shat upon, became shat upon, become shit on, will have been shat upon (the grammatically incorrect use of "shatting" is sometimes used in place of "shat" to express a continuing action)
*TF2 CTF*
"Oh shit, son, you just became shat upon!"
*Call of Campers; Modern Warfail 3*
"Become shat upon, kid! You just got 360 no-scoped!"