Detachment is a tool that you use when you still have to interact with the alcoholic. I don't think detachment is what you are talking about, it is how to move on from the relationship after it's over.
I know that up until my last relationship ended about eight years ago, I was always either in a relationship or working on getting into one. I'd been doing that from the time I was 16 until I was almost 50. I had completely lost any concept of who I was if I wasn't in a relationship. The relationship defined me in many ways. My career was important to me, but I had no personal life apart from who I was in the context of my relationship at the time.
This might be a really good time for you to focus on YOU. Try some new things, or try pursuing some interests you maybe used to have before you wound up in this relationship. It takes time to move on from a relationship that has ended--regardless of the reason. Make some new friends. Do some volunteer work. Take yourself out on dates (dinner and a movie--maybe all by yourself).
And give it some time. This isn't a race. It's OK if you feel crappy part of the time. Nobody enjoys feeling crappy, but it's part of the process. Eventually the good days will outnumber the crappy ones. Keep at it, and things will start to get better.