Given that introverts have limited social and emotional resources, before they need to reload, (we don't rebuild, we reload) we need to choose the best ways to expend our energies. In a church setting, introverts might desire to meet people, get more involved, and go deeper into the community, but we might not know how. It's intimidating because we don't want to waste our energy in less than purposeful interaction.
I want to propose an idea: make friends in high places. If you are new to church, find a person who has two qualities: 1) Is well connected in the church and 2) Is hospitable to newcomers. These people aren't always easy to find, but a good place to look is to the evangelism committee, if you church has one. Generally these people will be extroverts who are eager to meet new people, but aren't always great at actually doing it. Other places you could look to are people who are involved in new members classes or to greeters or ushers.
Introduce yourself; tell that person that you want to get more involved but you're not sure how. If you feel comfortable invite that person to coffee or catch them at the right time when you can have a one-on-one interaction. Tell them about yourself and what you're interested in. Ask them if they would introduce you to some people.
As a pastor, it has not been difficult for me to meet the right people, because the right people search you out. As a parishioner, it's more difficult, but I think this strategy will help.