Should I apologize ?

My girlfriend break up with me 10 days ago and already tried to contact me twice since then...
During the conversation (on Skype by the way, cause she told me she is feeling weak when she around me and can not tell all this in my "beautiful eyes"..)...so during the "break up" process she told me at least ten times how much she loves me, she will miss me, all this stuff and "let's be friends" of course...

The first time she called me 3 days after. The first thing she asked if I am angry at her ? I told her "Not, I not posses you and respect your decision. Though, I sad and disappointed by the way you did it"....After that she told me how much she sad, how much it is hard to her to break up with me, that she loves me very much and all this stuff...of course let's be friends again. At the end she told me "I love you, I miss you and you will be always on my mind", when I heard this I became really angry and reacted: "What do you mean by 'always on your mind ?', when you will sleep with your next boyfriend you will think about me ? ". Of course she didn't like it and said that she p*ssed now and we finished our conversation on this note. 3 days later she called again, but I didn't answer the phone...
I do believe that she loved me and it was hard to her to break up with me (may be I naive, though :) ). I know that it was not nice to say what I said, it's like I doubt her feelings. so should I apologize for what I said ?

Wow, okay. The "beautiful eyes" thing is full of crap. She just doesn't have the courage to say it to your face. Saying it through Skype, email, the phone, etc., are simply different ways of displaying her cowardice.
If she loved you as much as she claims, she wouldn't have broken up with you. I kind of wonder if she even knows what she's doing/saying. She may say she loves you now, but what you said back to her is true. Would she think about you when she's sleeping with her next man? She seriously needs to know that she can't have both you and the next guy.

I wouldn't apologize. She's just trying to keep you around in case things fall through with the next guy. Next time she calls, tell her you don't think the two of you can continue to be friends under these circumstances, then stop talking to her.