I too am single and, oftentimes, sit by myself. My purpose in going to church is to worship God. When I see others sitting by themselves, I go over, introduce myself and thank them for joining us that day. One woman broke down in tears, saying that, up until then, no one had ever made her feel welcome in any church. She, and a few other single women, are now my pew partners. Give it a try! You may discover a new friend in the process.
Going to church...you submit yourself to God, you worship God, you serve God. It's very easy to find fault with churches (this thread is chock full of them), but what it boils down to is that it's more about what you want and less about what God wants.
I am also single and go to church, like you, to worship God. I have learned over the years that if you want friends, you have to extend yourself in friendship.
It is never easy to be single and a member of the Church. While the Church rightly must focus on both the married as well as priestly/consecrated life, those who are single either by choice or circumstances are the most forgotten members of Christ’s body, the Church.