If a friend betrays you, and you tell them how you feel but they think they did the right thing, what next?

How do you move on? I have told her (them) my feelings but they do not feel sorry. Is it possible to move on? Perhaps by being more like acquaintances, or by not expecting them to value our friendship the way I normally value my friendships? Is it fair to continue the friendship if I still harbour these feelings of betrayal?