What makes me an introvert isn't that I am shy (I am not), what makes me an introvert is that I find all interaction with other people except a select few exhausting and draining. Don't get me wrong: That doesn't mean I am weird or bad at talking with people — in fact I am quite the opposite. It just means it costs me a lot of energy, while extroverts appear to lose energy when they are alone, I lose it when there is a certain kind of social interaction needed around me.
So people don't really see me as an introvert, because to them it is all about being shy and a little bit awkward. But that isn't what makes you an introvert, the energy part is.