To be detached in a loving way, doesn't mean your still not going to feel hurt or anger times.
To detach from someone means that you no longer delude yourself into the belief that without them you will no longer be happy.
You leave the person free to be themselves, have their own thoughts, indulge in their own tastes, follow their inclinations, and behave in ways that at the time are to their liking.
Even though what they are doing is selfish and often not rational, you set them free and move forward with your life, not on, just forward in the hopes they will one day see for themselves that there is a better way to live.
Life does not stop. Keep moving forward and allow yourself to feel this way, your human not a robot. Detachment is not meant to deny or disolve your emotions, it puts them in perspective.