It is never easy for men or women when relationships come to an end.
What I would suggest is try talking to her (and listen) and ask her why she needs the space. If she is saying she can't see you anymore it really just means that she isn't ready for a serious relationship and that isn't fair to you. It isn't easy when one person has more feelings for someone than the other. Many people in their 20's are still trying to figure out who they are and what they want for themselves that is why the divorce rate is much higher for people who marry before the age of 27. People who marry after age 30 have greater success because they are established in their careers, have had a variety of dating experiences (maybe and maybe not) and have pretty much figured out who they are and where they want to be in their lives. Sometimes both men and women are already buying their first homes at that point as well. So, she may be going through that. She may feel that after such a long relationship that ended (so therefore didn't work out) she is finding she needs time for herself.. to take care of herself before getting serious with someone again. If you really care about her you will give her that time. Maybe wait six months to a year and if you feel you have gotten past the relationship and have accepted it and moved on, see maybe if she wants a friendship.
Remember, if you really care about her you will see that this is an emotional need that she has..
Hope this helps..
If you have an interest in travel. Take time for yourself and do some back packing trips to different countries. I know a few people in their 20's who are doing this rather than having relationships and they are really enjoying life..