I am not entirely certain there is a great deal of assigning for blame for the death of Eliezer's father. I think that the overall blame would go to the Nazis, and those who inflicted unspeakable cruelty. Having said this, I think that Eliezer endures a great deal of guilt for not doing more to help his father. Eliezer knew of his father's debilitating health and understood that his condition was worsening. While he was loyal to his father, the survival instinct had overtaken him. He does note that he feels ashamed at his own sense of relief when his father was not in his bed the next morning. I would probably say that if there is any blame Eliezer assigns, it might be to himself.
In Elie Wiesel's account of his life in the concentration camp in the book "Night," he tells how his father and he were together in the concentration camp. The German soldiers had to move them from one camp to another. They made them walk a long way through snow. Many people had died along the way. Elie's father became weak and fell in to the snow shortly after they reached their destination. Elie left him outside and went in the barracks. Later he sees his father as he is walking from the showers. He leads him inside. His father is sick with dysentery. He has a high fever and is rambling. Elie lays him in a bunk. A doctor is around but his job is not to treat the men but to determine when to take them to be disposed of. A Pole and a French man repeatedly hit Elie's father because he soils the bed and moans.
When Eli's father moans for some water an SS officer goes by and hits him breaking his skull and causing his head to bleed. Eli waits till the soldier leaves then looks at his father. Elie goes back to his bunk and sleeps. The next day his father has gone. He believes they took him to the crematorium during the night.
Elie never directly blames any one person for his father's death. It is later in life when he becomes a speaker and has written his book that he blames the atrocities of the Nazi's that he blames them for his father's death. He also carries self-guilt for many years because he did not do more for his father. He is like so many survivors of the camps and the Holocaust. He carries survivor’s guilt.