I am not angry with the person who hurt me. Instead, I am sad. Can you differentiate anger and sadness in the forgiveness process?
People have different affective reactions when hurt by others. As you say, sometimes people respond with sadness, some with confusion, and some with anger. I focus on the theme of anger because that is the one emotion that can deepen and cause even greater pain than currently is the case. People who are sad can and should go through the forgiveness process if they so choose. Going though the forgiveness process should lessen the sadness, even if it will not eliminate the sadness entirely in all cases. People who are very angry and who have been so for a long time should especially think about forgiving as a protection for their own well-being, as well as for the possibility of a renewed relationship, if this is a goal. Deep and abiding anger has been shown to relate to a number of mental health challenges as seen in the book, Forgiveness Therapy by R. Enright and R. Fitzgibbons (2015).
For additional information, see The Four Phases of Forgiveness.