When we truly disengage from the drama and the narrative we create around the feeling, when we enter into an awareness of the feeling without judgment, without opinions, and without labels, we encounter the feeling itself. And that may be very different from what we imagine the feeling is. Zen Master Bo Mun likes to say, "Don't give back to the pain any more than it gives to you." If you have a pain in your leg, you may be more aware of your feelings about the pain - your fear of pain, your anger at being hurt, your desire to be free of pain - than you are of the pain itself. The pain is simply pain; what we give back to it is our opinion of the pain (we don't like it), our judgment of the pain (it's bad), and our label for it (the word and concept of "pain", with all the emotional freight that goes with it). When we are present with the pain in this way, without concepts, opinions, and judgments, we are present with it in true mindfulness. And free from our opinions and judgments, the pain can simply be there and show us its true face.
We can practice mindfulness with either emotional pain or physical pain; the process works the same way with both. One helpful way of accepting pain is to confront our (possibly unconscious) sense of entitlement that we be 100% pain free all the time. That's simply not a guarantee anybody has in life and when we look at it that way, we let go of our unreasonable demands on reality.