Oh, sweety, my daughter just had a similar thing happen to her, she is 13 by the way. I am so sorry this hurt your feelings. But let me put it in a different perspective.
Your friend was in the play, if she did not show up they may not have had anyone to take her place (this was the case with my daughter's friend), she had an obligation and responsibility to be in the play.
Maybe, just maybe, she did want to come to your party and her mother told her that she could not because of her responsibility with the play.
If she is your best friend she will be your best friend for a long time, a play only comes once. You can do something special for just the two of you for your birthday.
Yes, it is sad she could not come, but why don't you girls go to the mall, or something special just between the 2 of you to make it up. She might feel bad about it too.