An interesting topic. I consider myself an introvert too, sometimes behaving like an extravert. It largely depends on my energy level.
And here's the thing: if the gig is good, then you're not only sharing your energy, but also receiving a lot from the audience too. And the better the gig - the stronger the flow.
So that means a gig should be really good. Otherwise think of it as just another rehearsal with your bandmates when you're getting paid!