I'm not going to continue to talk to a girl I've been interested in after being rejected
Why aren't you going to continue talking to her? Did she say she does not want to talk to you?
I can't be friends with someone I was interested in
It is not a good habit to get into ignoring people. Even though the girl rejected you, being able to be mature and still talk to the girl is a very mature thing to do.
You should know that I want to get over her.
You do not have to spend time with her if you do not want to. Just understand that the mature thing to do would be to not ignore her.