As a dad, if you're young and in the earlier years of competition, I think it's perfectly ok to cry. It's not healthy holding in your feelings. It's only an embarrassment if you think of it as such. It's only natural to react that way. In contrast, if you throw a fit or take your frustration out on yourself or someone else (including your coach), that's an embarrassment no matter who sees it. Of course, I can only speak for my own opinion.
With that said, for many, the need to cry in sport (unless due to physical pain because of an injury) will lessen or diminish in time and in maturity. Just remind yourself that everyone has good days and bad days. Even after a bad event at a meet, nothing should hold you back from throwing super routines in the next rotations. It's all about your attitude. It's all about looking ahead and learning from your mistakes.
Just to share my personal story with you...
My 13yo L7 is not a super athlete (gymnastics and others) but she is good at what she does (with some potentials to make it big -- currently with another sport and previously with gymnastics). She definitely has her share of bad days. Even though she rarely cried at practice/training, she used to pour her eyes out every time she screwed up when things counted at a meet. The higher the expectation the louder and longer the cry, and the more massive the tears. I always felt bad when that happened but I was never embarrassed by her crying. But, one thing I can always count on has been her perseverance. Often she would outperform herself in the next events after mistakes are made. With it comes to crying, it suddenly stopped when she turned about 10 or 11. When she choked at the big events (including missing 1st in a particular state event) she is now ok with the less than favorite outcome and she would head right onto the next event with the best she got. She would even joke about the misfortune or mistake openly afterwards. I, OTOH, still have trouble getting over these incidences.