I have liked this guy I met through some friends for a couple of months, and he also liked me for a while. We hung out and got to know each other better and we have the same interests and everything! However we were worried about getting together because he was going to University and we didn't know if we would be able to handle the distance, but we gave it a shot a few weeks ago, and I have really fallen for him. He went to Uni shortly after and broke up with me a week later because he said he "can't handle the distance, but he would like to stay friends". I've thought about it a lot, and I really do like him a lot considering we weren't together for very long, and he is continuously apologising to me on the phone, and I just want to know if its worth trying to get him back?

No! Respect what he said. He wants to stay friends. Distant relationships are hard and when one is in college that adds to it. He recognized that and told you.

I do respect his decision, but how do I make sure that we stay friends without seeming needy and texting him constantly?

You stop texting constantly. You get a life apart from him then you won't have time to text him.
You tell yourself there is nothing there but friendship and deal with it. Go out with friends have some fun.

The best way to handle this is DON'T remain friends. You can't handle that . Few people can. You have fallen for him, so to be a friend means you have to see him dating others, maybe getting involved with someone else. Can you handle that? I couldn't.