I'm certainly introverted and I think one characteristic of introverts is being misunderstood. I've been told that extroverts gain emotional energy through social contact whereas social interaction costs introverts emotional energy. So it's not that introverts don't like social contact, they just can't take too much and need their time alone to recharge.
Last Saturday I went to a friend's wedding with lots of people I didn't know. I play music with the groom and so after the speeches a PA was set up and a group of us played for a couple of hours. I had a great time - not the least because of the great 'Mark Bass' rig I borrowed - and was feeling quite outgoing. The next day my wife visited relatives and I was alone for most of the day, which was just what I needed. I really wouldn't have liked a repeat of Saturday. I pottered around doing jobs, watched a bit of cricket and had a very low-key low-stress day.
I also prefer to observe alone (though I rarely get the chance) to recharge the batteries and have some quality 'me' time. And, although I can't stay up late too much anymore (lack of sleep triggers my depression) I can fully relate to staying up late to get some quality solitude - I used to do it all the time.
Regarding playing music to crowds: I hardly ever get the chance but to me it's still mostly playing with friends. I'm sufficiently amateurish that I need to concentrate on what is happening on stage and the sound is usually so poor that hearing the others takes an effort, so there is little chance to even notice the audience. I don't know what would happen if the sound was great and I was confident of every song and so could focus on the audience. Perhaps that is when I would freeze!