Do your palms sweat, your heartbeat accelerate and your mouth go dry when you're about to give a speech, even if for just a few listeners? Don't worry about it, evolution is to blame.
You feel like you're in danger. Your stomach pulls down, all your senses engage and your muscles tense up. Your attention is only focused on the thing ahead of you. This is an example of our prehistoric ancestors' typical reaction to a predator's attack that could come any time. It's the well-known "fight or flight" reaction.
Evolution has shown that people can defeat larger and stronger creatures thanks to cooperation and the ability to create tools. The same applies to public appearances.
If you're too worried about spoiling your performance, you'll wind up spoiling it in the end. Then you'll be more and more afraid of your next performances. How can you get out of this vicious cycle?