One of the behaviors that displays self-pity is trying to get attention from others because of their particular difficulties often exaggerating the severity of it. For example, perhaps they have a minor physical difficulty - letting everybody know about it so they can get attention. Sometimes it's as if the smallest problem is very great. There may be a lot of feelings that "nobody is as bad off as me" yet they're actually not having many difficulties compared to others.
The antidote to self-pity is opening out to others, that is, universalizing the particular difficulty that we are experiencing at the present moment by using it as the base for what we call the "D/D" technique. This is a Defusing/Diffusing Compassion/Lovingkindness meditation technique. For example, say we're afraid, we have some fear about something, even something very small. Rather than pushing away the fear or trying to talk ourselves out of it we can actually use the fear by noting it, trying to feel how it feels in the body, the tension, the agitation, trying to have compassion for yourself and then thinking of another person in the world, same age, same sex, who may be experiencing a similar fear. Understanding how it feels, try to have compassion for them. Then think of another person the opposite sex of similar age in the world, who may be experiencing fear, feeling compassion for them. You can go up and down in age and gradually contemplate people in situations where they will experience more intense fear. Feeling compassion for them.
Often times we only create situations to be afraid of in our mind, which in reality are not that frightening compared to actual experiences many people are confronted with which are even life threatening.
By actually allowing ourselves to contemplate situations that are much more intense and to consider people who have much more intense feelings of fear, allows us to see the universality of fear and tends to lessen our fear towards things that are not so fearful.
Self-pity is more the "poor me" type of idea in the mind such as "oh it's so bad, oh it's so overwhelming, nobody is as messed up as me". Or "My particular situation is the worst thing in the world that could happen..." when actually it's not.