After Eliezer and his father have spent the entirety of their concentration camp time together, Elie's dad's death is rather unemotional. There is little in the way of a teary goodbye, although Elie's dad's last word is his son's name.
Elie awakens the next morning to see his father's bed inhabited by a new invalid. He thinks upon the fact that his dad may have been taken to the crematory while still breathing, and he reflects on the fact that his father will have no services to mark his death.
Elie does not weep, and expresses regret that he did not respond to his dad's call. Yet, as Elie says, he had no more tears. And, as he admits, he is happy to be free of the burden of caring for his father. Both actions may seem harsh, but they are also understandable given the context. Elie does not weep because he has become desensitized to death -- something he has seen as a daily event. As for feeling free, this is also understandable. While his father has seen him through difficult events, of late, he had been more of a burden to look after. When Elie leaves the concentration camp, he later grieves his father in ways that are more "human" and appropriate. I believe he acts as honorably as possible in an inhumane environment.