Failing in public means you also get to rise in public. Same audience, better ending.

Visibility cuts both ways, and people forget the second half. The same group that watched something go wrong is still watching, which means they are also positioned to see what you do next. Private failures get no witnesses for the recovery either. Being seen at your worst is the cost of being seen at your best, and you only paid half of it so far.

Rather than trying to make people forget, give them something new to look at. Show up to the thing you were embarrassed at, on time and prepared.