First off, you should be careful when using apologic statements at work. They can be seem as an admission of guilt by the claimant and/or employeer and can lead to further action. Saying things as such as:

(1) "I understand that you feel that way, but my intention behind that statement was ... ." (2) "It's unfortunate that you feel that way, but my intentions were ... ." (3) "I can see that my actions have affected you, by my intentions were ... ." (4) "I didn't intend to upset you, my intentions were ... ."

would be better for issues in the future.

In regards to how she responded. You can't control how people interpret and handle situations. You can only change with how you deal with it in the future, knowing that she has responded this way should let you know that (

I would from now on keep all conversations in written and storable form via email, letter, or chat, and if you need to talk to her, make sure you plan what you are going to say and make sure you have another colleague in the room as a referense to the conversation.

If you feel you want to remedy to the situation, I would set up a meeting with HR and try and come to a solution.