Most of the embarrassing situations you’ve been in have only been embarrassing because of what “you think” other people are “feeling”.
In other words, it’s only “assumed empathy” that makes things embarrassing. The fact you tripped up the stage is only a cause of embarrassment if you think other people will be imputing embarrassing feelings onto you. If you were totally convinced that no-one saw you, or that everyone thought you didn’t trip, would you be embarrassed?
The trick to dissolving an embarrassing situation is convincing other people that you’re not feeling embarrassed… to stop them feeling empathetically embarrassed on your behalf.
One way is to simply laugh it off. Another way is to tell them that your not embarrassed.
I do this with my stutter when preaching. I tell people that I’m not embarrassed about it, I make them feel at ease – not about my stutter – but about how I feel about having a stutter. Once they know that I’m really not embarrassed about it, neither are they.