Most people try to ignore or suppress their negative feelings. Then they are haunted by ghosts day and night, and these negative feelings become the demons they project into the world of action.
Instead of trying to ignore or suppress negative feelings, welcome them into the space of awareness. They are legitimate parts of your being, your energy, your body. Anger, jealousy, grief, fear of failure, loss: Whatever feeling arises, let it crystalize into a concrete mass of energy, felt as sensation in some part of the body.
Embrace the negative feeling without resistance. Bathe this bundled energy in the clear waters of awareness, simply observing it. In its own time, gracefully, the negativity will unwind and release back into the useful energy of aliveness. For it was never a "demon," never a "bad" part of you. It was just bound-up aliveness, waiting to dissolve into joy.
Only when we let negative feelings solidify can they dissolve into the clear brilliant sky of compassion. Here is a useful guided meditation by Sri Sri to deal with negative emotions.