Melissa Rivers Kathy Griffin 'S*** on My Mother's Legacy'

5/14/2015 6:09 AM PDT

Melissa Rivers believes Kathy Griffin is self-centered beyond words ... so worried about saving her own ass that she would crap all over the legacy of Joan Rivers.

Rivers was at the 92nd Street Y in NYC where she sat down with Hoda Kotb to talk about her new book. When Hoda zeroed in on "Fashion Police" -- Melissa had trouble harnessing her anger.  

Melissa believes Kathy more than disrespected Joan in the way she handled leaving the show, saying she "s*** on her mom's legacy."  And she didn't stop there.

Our photogs got Griffin out Tuesday night and asked her about Melissa's comments ... but she wanted no part of it.