You absolutely did the right thing by telling her that you need a break from her.
Ideally you would respect that she's not wanting to date you and let her go. Ideally, you'd use this space and time to let your feelings go. Yes, it's OK to be sad that it didn't work out - but you need to listen to what she's saying.
However, it seems that you don't want to take the sensible route and that you are hoping against hope that she will change her mind. If she's to miss you, the only way for this to happen is to not be there for her. She can't miss you if you're still around! If she still tries to contact you, tell her straight up that you had feelings for her but as they aren't likely to be returned, you need time to let them go. Most importantly, don't take her 3am calls. If you find you can't refuse them, then turn your phone off at night.
Lastly, she drinks too much and needs to talk at 3am. Mate, only broken people do things like that. Yes, I get that she's still grieving - but if her grief is causing this behaviour, she's nowhere near ready for a relationship.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.