For me, concert performances never bothered me. Sometimes I was just eager to get the event over because I hated wearing the required tux.
However, solo recitals freaked me out. I had one senior recital for my undergrad which went decent. I wasn't super happy with the way I played... but I always got kind remarks from faculty and peers. I had two recitals for grad school and I was very nervous before the first one. I also wasn't prepared for the endurance for a full hour long of solo work. I got tired towards the end (mentally and physically) so the mistakes started creeping in. The second grad recital went great. I was super nervous, but once I got on stage I just focused on the music. Somehow I was able to just relax and play. Sure there were mistakes, but I was able play musically and make a good impact on the audience. If solo playing is what makes you freaked out (like me) then I would suggest playing in front of various groups of people. Friends, family, at school or church. The more you do it, the more comfortable you'll become with it.
My granddad was a very accomplished conductor, and he still had an upset stomach due to nerves before every concert he was conducing... so I think so of it is just natural.