Well you need to do some thinking.
First of all, you need to think just how much you like the girl that you broke up with. See if you just kind of like her... or if it is a very strong feeling.
If you decide that it is very strong, then you need to think about something else. Is it worth pursuing? If you think it is... you need to give her space. After you giver her some space. Tell her that you would like to be friend, but you feel as if you should explain yourself. Tell her that YOU were wrong in doing what you did. And that it didn't matter what her friend said... and that you shouldn't of listened anyway. That you have learned a lot from it. Learned that you should confront her about things and trust her.... not others. Basically, tell her that you realize you were wrong... and you now want to be right.
If you don't think it is worth it. Then YOU need some space. Don't date anyone. The worst thing to do when your mind is on an ex is to date someone else.