Perhaps the point is that we have a false view of heroes and heroines, but that living through war destroys people (even the survivors) and that there we should not be so quick to glorify it. By any measure, Katniss demonstrates bravery, courage, perseverance, and other traits that we would call heroic. But she is no hero. She is so badly abused and manipulated in so many ways and for so long that we should not expect her to overcome, but that we can only be glad that she survived at all.
The most heroic thing any of the characters can do is to memorialize the past while taking their pain and grief to the grave in order to protect the next generation.