How do you deal with failure?

[windshieldbug]

Find out what the committee was listening for

After having sat on a few committees, this is the biggest and hardest. Normally, in audition committees of a professional orchestra the Music Director has 51% of the vote. So you have to crawl inside their head and figure out what kind of sound/blend they're looking for. Even if the final is a series with the orchestra.

If you can't play the required pieces well, you wouldn't have been invited in the first place.
After that, it's how well you work with the section.
There is always something that you could have done better, or something that you haven't picked up on yet.
This is your opportunity to identify it, and work on it.

The first round of the Philadelphia Orchestra audition, nobody won (including candidates that had played well with the orchestra as subs). You never know what the committee is listening for, or what may impress them.
Playing everything well is only the first hurdle...

If you fear rejection, DON'T go into music at ANY level, no matter how much you like the applause when you do something well! An audition is like a job interview, and being qualified only gets you to the next level.

[DHMTuba]

“It is hard to fail, but it is worse never to have tried to succeed."
Theodore Roosevelt

[eupher61]

Fail. In whose ears? Yours? Maybe that's a fair evaluation, if you know you could have done better, but simply did things incorrectly.
The committee/listener's? Not at all fair. If you performed the best you were able, and know for a fact that your performance ability is at or above the level reasonably expected, it was a difference of opinion.

If YOU think you failed, you can do one thing: prepare again, do another audition, and do your best. If you simply did not achieve the goal of the audition, the needs and demands were a little different than you expected. Try to find out what the difference was, and work toward having that as part of your arsenal.

No matter what, you can quit, or you can go on. Taking it as a personal affront will accomplish nothing. Observe, learn, and do. Don't be judgemental about yourself, or others...simply work to achieve the ultimate goal.

"The Cow in the Parking Lot" Edmiston and Scheff The focus is more toward anger, but your OP comes off as angry. That doesn't help anything.

[Mark]

Like if you failed an audition you really cared about...

Failed? Or didn't win the audition? To me, there is a big difference.