The most obvious step to take is not to write the self-pity. If you write about your characters getting on with their lives, they are getting on with their lives. First, cut out all (or almost all) "told" emotion ("Mary felt miserable") if you've written any. (Almost always good advice.) If the scene is now emotionally flat, replace it by an action that shows the emotion ("Mary sat there, silently, picking her Kleenex into tiny shreds.")
Then - except in scenes where you want self-pity, cut out direct ("How can I go on? she thought") and indirect ("How could she go on?") inner voice that exhibits it. Replace it, if called for, by action-oriented inner voice ("She would get a new coffee mug as soon as the store opened. And a pistol.") And make her get to her feet and do something - write more actions. ("She took out the broom and swept up every mote of the broken mug, sweeping away what she promised herself would be the last trace ever of John in her life.")
Dialog - as always, never have two people quite agreeing with each other. The two people in an interchange are each having a slightly different conversation. A says P; B hears it,associates it with Q, and answers that, and so on. If Mary tells Pauline how much she valued the mug that John broke, and Pauline tells her about the article about decluttering in Home magazine, Mary's pity party has been cut off.
Good luck...