I would venture to say that if you truly are an introvert (being social saps your energy) then you should consider social dancing or rock climbing, because for a few minutes at a time your attention is focused on just one person and you can for the most part shut off everyone else, unlike being in say a generic 'common interest' meetup.
But anyways you have to actually put effort into it. Unlike the olden days, where everyone in town knew what was up, and dragged other people around, or college, which professionalizes the student's entitlement to experiences, you are rarely going to be handed social activities on a platter.
If someone invites you to spend time with them in a group, make a mental note of it, and if you're counting too many examples where you're saying no, think hard about saying yes the next time.
Also, yes, it is harder being an Asian. I know this from personal experience. But there is nothing you can do about that, so forget about it.