Introversion has nothing to do with being anti-social. An introverted person can be as sociable as an extrovert. The main difference is that the introvert doesn't get energised by being around other people; they need time alone to recharge. An extrovert is the opposite - they're tired by spending time alone but recharge in social situations.

Susan Cains book "Quiet" is an exceptional exploration of the field, and well worth reading to breakdown some of the misconceptions about introverts.