It's all a matter of perspective. My uncle once brought his kids to see a big show I was in, and afterwards said just what you did. I looked at him, genuinely surprised, and said something like "dude, you're a surgeon. If I screw up at work 2,000 people laugh at me, and forget about it five minutes later; if you screw up at work, someone dies. You really think I should be the one feeling nervous?"

You're right about training and experience, though. I screwed up on stage (in loads of tiny ways, not usually perceptible to anyone but me) every time I ever stepped onto one, and in big ways lots and lots of times as well. But, you know, I always knew that I (with my castmates' help) would get out of it. Failure is inevitable, and it doesn't matter. In fact, if you haven't failed somehow, in at least some small way, then you either don't know what you're doing, or you aren't trying hard enough to succeed.

Also, when I was training young actors I always told them that they will never experience such unconditional love as when they first step in front of an audience. Those people have given at least their time and maybe their money to see you - don't you think they want you to succeed? They're rooting for you, none more so.

To bring this back to the larger subject of the thread, I think all of that's also true of every job interview any of us will ever attend, or conference paper we'll ever deliver. It'll never be perfect, and that's just fine.