Remembering that Elie Wiesel is actually a Holocaust survivor, and that the story is his own, he is writing from his own experiences and beliefs. Desire for revenge was not one of the emotions he felt, or at least not immediately.
Consider all of the energy and emotion Eliezer had expended simply to survive, just to get to that point at the end where liberation was even possible. It may well be that he simply wasn't capable of rage or revenge at that point. Furthermore, consider all that had been lost by him in the Holocaust and the camps by early 1945 when the story ends: most of his family, his confidence, his identity, his health, his psyche. So much was lost by him, and every other survivor of the Holocaust, Jews and non-Jews alike, that they had to be in severe psychological, emotional and physical shock by the end of it.
Somewhere, in wading through the complex maze of emotions associated with such a horrible, sustained trauma, I'm sure there was a desire for revenge. But that stage of his mourning just hadn't had the chance to develop yet, at least, by the end of the book.
The most obvious answer to this question would be where does Eliezer begin to demand for revenge? Where does he start? When the narrative ends, he stares back at the reflection in the mirror and cannot recognize the figure he sees. How can revenge be formulated at this point in time? In order to demand revenge, one has to have a sense of who they are and how they have been wronged. Eliezer had been wronged in so many ways, had his trust violated in so many different manners, and had endured so much that there is no effective place to begin in demanding revenge. Does he spit venom at the Nazis? Does he demand justice from those who were in the camps and simply tried to survive without the acknowledgement of others? Does he seek reparation from God, whom he believes cursed him to endure such an existence? I don't doubt that there is anger and some desire for justice on a scale of personal vendetta, but how could he articulate such a condition when the liberation from the camp results in such an existence where so little can be grasped effectively? It would be naive for the narrative to end with him seeking revenge against those who violated his faith, broke his family, killed his father, mother, and sister, and broke open any hope at salvation. It would take away from the picture of horror and cruelty that had been created. If we really wanted to take this to a transcendent level, Elizer demanding revenge would undercut the idea that had been present that evil is something that has to be stamped out and opposed at every turn. If Eliezer seeks revenge, it would be harboring a type of hatred that had condemned Eliezer to have to endure what no other human should.