Suzanne Collins doesn't so much justify the sacrifice and death that occurs in the story as much as explain how such things can happen. The abuse of power in the Capitol is the catalyst for the violence that occurs in the story. By setting up the Hunger Games for their own amusement, they have set into motion a cycle of violence, sacrifice and death that only ends temporarily each time a victor is declared. The people chosen to compete in the Hunger Games, called tributes, are forced into a situation where violence is their only chance at survival. To be peaceful is certain death.
Although violence is prevalent throughout the book, we do understand the need for those who are not in power to use it. We are on Katniss' side as she uses violence to survive and to defend her friends. We recognize that she has no other choice, and given that there is no peaceful option, we are rooting for her to survive by any means possible. At one point Katniss even uses violence to end the suffering of another tribute. Cato has been mauled by dogs and is in devastating pain as he lays dying. He begs for someone to help him, but there is no way to save him. Katniss chooses to shoot him in the head with an arrow to end his pain. It is violent and sad, but we can understand that she did it from a place of compassion. We never think that violence is okay, but we understand that the weak, in terms of power, are given no choice when it comes to using violence to survive.