What is required is repentance, which is an act of the will. Remorse and regret are emotions, which you may or may not feel and do not have control over. Feelings of remorse and regret are not required, but they are helpful in keeping us from sinning again. One way to encourage such feelings is to develop a devotion to Christ’s Passion. Meditation on the agonies Christ suffered to merit for us the grace we receive through confession helps in developing a horror for sin and a just remorse for the sins of one’s life.