I am an introvert coming out of my shell and doing well at learning the art of socialization and trust me, we have it way better than the extroverts do. But there's some things you need to clear from your head before you start thinking about success with women.
First off, you have to accept your introversion as a gift and start treating it as one instead of being worried about how different you are. You have to understand that spending time with extroverts is the only way to learn about them, and eventually you will learn more about people. You will never have any trouble socializing with an introvert, so if you want to start using your gift to land some chicks then you might as well start paying attention.
Your advantage over extroverts is that you do not depend on others for your own emotional support. This is kind of rare among people and women can sense this and are attracted to your inner strength. But they won't be attracted to you until you feel comfortable with this, because in turn they will feel comfortable around you.
I'm calm, comfortable, often quiet when I don't feel like saying anything, but I also reassure these people that I care what they're saying by laughing or advancing the conversation. Not because I feel like it's right, but because that's what makes people like me.
Extroverts can sense introverts and although they may not understand them, some recognize that they're probably smarter and are usually jealous to some extent if they make rude remarks about you. If women sense this in you, it's attractive and once you start trying to get better at socializing, you'll learn what makes people like you and master these techniques when spending time with women. Once you can combine this with your sexuality, you have a formula for success. I don't approach women often, but constantly have women gravitating towards me because I have started to force myself to learn all this.
Just stop taking your introversion so seriously and start seeing social gatherings as opportunities to learn more about people because you have to give a little more than you get back in order to get a women's physical love.
The last statement may come off wrong, but when you find it hard to care about the woman as well as the sex, these efforts don't come naturally.