First off, this point needs to be reiterated. There is a lot of assumptions in to the supernova, and we don't have all the facts. So, assuming that the Federation is simply like *shrug* at the supernova is hasty, at best.So what do we know about the supernova? Not too much so i'm going to make some assumptions here.
Thus far, as people have pointed out, that's not what happened. A fleet was assembled, and it was attacked and destroyed. They said "No" to putting in more resources after losing so many. It has nothing to do with hate and everything to do with resource management.And now i' supposed to accept that the United Federation of Planets as depicted up to this point in all shows and movies would say no to a rescue operation