Please don't be hard on yourself, you are just being a good Mom! Sometimes I miss that sense of instant community for my kids. I'm also very introverted and find it difficult to go do social things. My almost 4 year old is super social and will be starting preschool this fall to be around other children.
Our local library has lots of drop in story times for babies-preschoolers that are free. And the YMCA also has some free parent programs where you will meet really nice people.
We also just head to the playground and my little guy plays with the other children there.
I wouldn't worry too much about socialization, my little guy is still super social and we didn't attend very many activities or have playdates. He talks to me a lot during the day, and I try and keep him busy.
The United Universalist church is for anyone, agnostic, athiest, Buddhist, etc. The children's group there might be fun.
When are you due? I hope your pregnancy has been going well.