I suppose this has happened to me many times before, much more when I was an AFC though because the women I spend time with now know I don't take 'girl drama'.
It depends on who the girl is and what you intend to have with her in the future. Do you honestly believe you can change things around and get into a relationship with her? Do you want to be just friends or still go into a relationship with her?
Now, either you said something pretty bad, or she is taking the incident way too seriously. Her comment of saying "she somewhat felt the same way" seems pretty arrogant to me. Just let her know that you are sorry for the way you acted and you would like things to go back to the way it was before, because life is too short to hold grudges and you thought your friendship with her was much stronger, that nothing could come between it. Give her some space, and than wait for her to start talking to you.
I know it may sound non-DJish, but based on the fact that you came to a message board for a problem, I'm just assuming that you are desperate to get things fixed, and what I stated above has worked for me.
Just avoid getting yourself in those types of situations in the future. Also, don't over-do the "sorry", since that is NOT what I am asking you to do, merely just say it once.
Oh yes, one more thing. You made a mistake by saying "you missed how things were." That just is WAY too desperate and by stating that, you are making her the prize. You need to regain your status and power in your relationship with her, until her head gets so big that you will have no chance of bringing her down to your level.
Men make mistakes, and real men acknowledge that they made those mistakes. They apologize, and they move on. Whether the person they hurt decides to forgive them or not, it's their problem, and real men do not care less how they feel.
If you state the above to her and she still reacts in a negative manner towards you, give this girl up. Make her realize what she is missing out on and start talking to new women, the jealousy factor might kick in. Besides, do you really want to "like" a girl that puts out so much drama?
Hope I helped you out, let us know what happens!