Sorry that you did not get in.
But one person saying, 'no,' is nothing.
In music - a lot of people will say, "FUCK NO." Get used to it.
That said...
You have the right attitude and idea - talk to the prof - ask when you can re-audition...and really fucking bug him to get another shot.
If he says it's a fundamental, "You just plain suck," then work your ass off, find a good teacher and fix it.
Very doable.
If he's just allowing another person in on a coin toss, IE, "You were great but so were X, Y & Z," then bug the living shit out of him to get another audition. Show 'em how badly you want this.
Do you have any clips?