Even very experienced and accomplished artists make mistakes from time to time. It is part of being human. It's going to happen. When it does happen, I try not to act like it's any big deal and I smile or laugh, maybe even make a little joke about it. I use it as an opportunity to compliment the person who did catch me, maybe say something like, "You are quite sharp," or "Wow you are very observant."
If you are humble and lighthearted about it, and do not act defensive, they will usually end up liking you better than they did before, and then reacting well to the next trick or tricks. Most people are aware of their own imperfections and vulnerabilities, so they can relate to us in a positive way when they see that we are imperfect and vulnerable, just like them and that we are not afraid to admit it. The idea is to entertain people, and help them feel good and have a good time - not to be super men or women.
Of course, I do try to to understand what went wrong and why, and to use it as an opportunity to learn. I analyze how I can fix it, how to improve my handling or my presentation so that hopefully it will not happen again. It might also be that the move or trick is not one that is natural or right for me, and if I realize that, then I stop doing it, and move on.