Put things into perspective. Casting a show is an extremely difficult process. Directors have to consider many aspects of auditioning actors besides talent, such as height, weight, the overall look and chemistry with other potential cast members.The most talented singer in the world could audition for the part of Johanna in “Sweeney Todd,” but if the director thinks she's too old or too tall, or if she doesn't look right next to the person cast as Anthony, chances are someone else will get the role.
Ask for feedback, especially if you know the director personally. Many directors are happy to give constructive feedback. Just be sure to ask respectfully, and state that you're asking in order to improve for the next audition. Whatever you do, don't throw a fit and scream, "Why didn't you cast me?!"
Take a good hard look at your own audition. Did you do your absolute best? Was your song choice appropriate? Did your cold reading go well? Focus on areas where you can improve for your next audition.
Polish up your theatrical resume and ensure it's current. Consider having headshots taken, if you don't already have them.
Brush up on your auditioning skills. Have a variety of songs ready and several monologues, at least one dramatic and one comedic.
Review any constructive advice you have received from a director who didn’t cast you. Focus on improving those areas of weakness.
Go to that next audition! Rejection is a necessary evil in show business. The more you audition, the more comfortable you become and the better chances you have of eventually landing that dream role.