I think it takes a lot of practice and experience to learn how to and be able to truly let your auditions go. Especially if it's a role that you really wanted or felt connected to. And even more especially if things are slow. It becomes easier and easier with time as you realize there will eventually be another one if you stick with it. For me, understanding that what's meant to be mine will be mine helps. I also have certain things I do right after an audition to help me put it out of mind. I wanted to share a few of those, which is particularly appropriate because I just got out of an audition for a film that had a script and concept that I loved.
1) Focus whole-heartedly on my very next task whether it be going to work, cooking dinner, cleaning the litter box, or finding my way way back home.
2) As soon as I catch myself analyzing any part of the audition I stop. I just stop. It's pointless. This is something else that takes time and practice. That being said, in the moments right after the audition is over I do think it's neccessary to note anything of importance. Like significant notes about the production team in case you are called in again or things that you learned worked or didn't work. But after that initial evaluation everything else can drive you mad and bring you down.
3) Make sure that once I have saved any contact information from the production team I delete any emails or voicemails pertaining to that audition. The heart doesn't feel what the eyes don't see. (Or something like that.) I won't throw away any physical sides or scripts yet, but I do tuck them away in one of my acting folders.
4) Look for more auditions of course!
5) Focus whole-heartedly on any acting related thing coming up including auditions, classes, screenings, events, rehearsals, and shoots.
6) Write in my blog or do something creative.
7) Remind myself that getting the audition in the first place is a big deal and means I'm doing something right.
8) It also helps to literally sing the words "let it go" while imitating Frozen's Elsa. Yes, you have to mimick her movement from that scene as well. Trust me, you will feel much better.
Update 05/13/2016
I wanted to add something else that has been helping me to let go of each audition; I now keep a handwritten audition log. I write down every detail I can think of about the audition. Those include what the project is, names of all involved, location, and pay, I even include what I wore and which headshot I submitted. After I write all the details, I am sure to add how I felt about my performance overall and things I could do better next time. And then of course, whether or not I ended up booking the job Many industry pros suggest doing this and I have to say it has helped me a lot, not only with letting go of each audition, but also with my confidence.
Update 05/13/2016
I wanted to add something else that has been helping me to let go of each audition; I now keep a handwritten audition log. I write down every detail I can think of about the audition. Those include what the project is, names of all involved, location, and pay, I even include what I wore and which headshot I submitted. After I write all the details, I am sure to add how I felt about my performance overall and things I could do better next time. And then of course, whether or not I ended up booking the job Many industry pros suggest doing this and I have to say it has helped me a lot, not only with letting go of each audition, but also with my confidence.