How can I get my girlfriend back after she broke up with me because I didn’t respect she needed space?

There is not a quick fix for your question which may feel frustrating. It sounds like you are having some struggles in your relationship and it would be helpful for me to have more information in order to really help or lead you in the right direction. However, I can point you in a direction to start working on it.

There are several questions I would ask in a session that you can ask yourself. How long have you and your girlfriend been together? Is this the first issue or are there other issues? Any history of infidelity or trust issues in this relationship? Is this your first relationship? If not, what is the history in the other relationships? Do you have a history of trust issues or infidelity? Any trauma or attachment issues from your childhood? Answers to any of these questions may be a starting place with a therapist. This can assist you and the therapist in determining a root problem in relationships.

I'm curious what is "causing" you to "deny her space." 

It may benefit you to focus more on working through your own relationship questions or history before focusing on getting her back. By working on yourself it will allow you to improve whether you return to her or not. If the only focus is getting her back, it may just be putting a bandaid on this situation and not assist with future issues. 

A therapist can help by working through these questions with you. They can inquire about the past and allow you the supportive space to process past events that may be leading to the behaviors she is unhappy with. 

I would recommend you start with individual therapy in order to look deeper into these questions about yourself and your relationships (both romantic and family). The therapist can assist you in resolving some concerns or learning skills to work through them. Then, if you and your girlfriend decide to work through this, you could start couples counseling with someone who specializes in that. 

I would be happy to assist you in individual therapy if you are interested.