Your ex girlfriend wants time to herself. When she told you that you saw any chance you may have had with her go up in smoke. How can you possibly get a woman back if she's taking time or needs space? It obviously means she wants to get away from you, right? It does. However, don't start a pity party in your own name just yet. You can actually use her need for some time to your advantage. You can get her back and even more in love with you than ever before.
If your ex girlfriend wants time to herself and tells you as much, agree with her that it's a great idea. She's not going to be anticipating this type of reaction from you at all. She may have actually been putting off telling you because she was deeply concerned there would be a great deal of conflict between the two of you. She knows that you still care for her so she'll be puzzled when you agree that time is a good thing. If you can have this conversation with her and not shed a tear, that's going to help you even more.
Once you two have agreed that taking time is a good thing, follow through with it. You have to make a decision to not contact her at all. The length of time you decide to do that is up to you. It's advisable to make it for at least two to three weeks though. This will ensure that she sees that you were serious about wanting the time to yourself and also about giving her the time that she needed.
During that time it's all about you. You have to make some positive changes in the person you are if you want to win her back eventually. One thing that most guys don't even think about after a break up is that the relationship was not working for some reason. You have to identify what that reason was and then you have to work on improving what you can about yourself to ensure the second time around goes much better than the first. If you try and start up the relationship with your ex girlfriend where you two left off, don't expect it to succeed. The same problems will pop up and the conflicts that plagued you then, will destroy things again.
You're going to think about your ex a lot during the time you two aren't talking and she's probably doing the same thing about you. Absence has a remarkable way of reminding us of why we love someone. If that person is no longer there, they weigh on your mind more and you can't stop thinking about them. That's what your ex girlfriend will be experiencing during her time away from you.
The combination of time and self improvement is a powerful one. All those anxieties she may have had about being in a relationship with you again, will have fallen to the wayside because of the longing she's feeling. Once you two do start talking again, show her how you've grown and matured. She'll be touched that you recognized what you needed to change and she'll be honored that you made those changes for her.