I don't know what the truth is, but doing something you aren't good at, and aren't improving at, is also draining.
Yes, I'm an introvert, too, and I understand exactly what you're talking about. The diff is that how much I'm "drained" depends on the group of people. I have quite a few friends with whom I'm close enough to just be myself, to not "act". They don't drain me at all. I just eventually run out of things to talk about, unlike the extroverts who find more to talk about.
A group of co-workers? That is tiring, because it takes a lot of effort to act that nice.