My wife and I are both introverts, and Disney cruises have been wonderful for us. As others have said, you can request a table for just the two of you, which we have always had honored at the second seating (not to say it wouldn't be honored at the first, but we're second seating people). Deck 4 always has lots of cozy quiet chairs to read and relax. The stone loungers in Senses are a great place for an introvert to zone out. The adult only pool area is quiet and peaceful even when there's other people around. Even the lounges at night tend to have spots where you can quietly converse and people watch. So even on a crowded ship we've found that there are plenty of places for peace and quiet.
Introverted as we are, we DID one time find ourselves in the big chairs of Match Your Mate, where we ended up becoming...ahem...infamous for the remaining 6 nights of our 7 night cruise.