Why didn't you get the part? Maybe you auditioned the best, but you still didn't make the cut? What goes on behind the scenes that you don't know about... Let's take a look and see how you can get the part next time.
1. Wrong type
You aren't right for the show or part you're auditioning. And it may be that you're perfect for the part as it's been played before, but now the director has different vision. What can you do about it next time? Make a strong choice with the character. Regardless if it fits the director's vision, show you can go for it. And what if you're not necessarily the right "type" for the part historically? Again, make a bold choice and stick with it. At the very least you show you can audition and will build a great reputation (see #3.)
2. Already cast
You might not know it, but the part could already be cast even before auditions. I know it stinks. But it's the reality of theater. Take pride in knowing you had the opportunity to get your face out there. You could have the very best audition of your life, but the part is already going to someone else.
3. You need more experience (and reputation)
This is where auditioning often comes in handy. The more people you know in your theater community (and who know you), the more your reputation grows. So make sure you audition as much as possible. Director's don't like a lot of risk when it comes to casting brand new actors they haven't heard of before. They want to know you're professional, and will commit to the show.
QUIZ: Who would you rather a cast?: a talented but "never-heard-of-them" actor OR a slightly-less talented but "great-reputation-and-awesome-to-work-with actor" ? ... I promise reputation will outweigh talent more often than not.
4. You auditioned poorly (you weren't prepared)
It happens, you show up to an audition and completely bomb. It could be for a number of reasons, but most likely you weren't prepared. It's a great lesson to learn -- always have your monologue, or song, or accent, or resume ready to go. Director's can smell unprepared walking in the room. This is one of the greatest Catch 22's of the theater. How do you become prepared? Well, besides have your monologue or song practices, and your resume ready to go... you audition, a lot. Auditions are part of the art.
So how do you get the part next time? (And there will ALWAYS be a next time)
Audition often! Get rejected often!
It is the ONLY way to get good at your craft. Start thinking of auditions as experiments, get comfortable in them, and try new things. Use auditions to make bold (prepared) choices.