There was no sacrifice, that is later Christian belief. There was just a death. The Bible makes it clear why Jesus died, because the Jewish leaders murdered him. The gospels say they hated him. He said: "Why can you not hear my voice? Because you don't have the truth in you. You are children of your father, the devil, and the works of your father you will do."
Actually, that is not why Jesus died. You are right, the Bible makes it clear, but not for the reason you are stating (also, one can be fully sure that Jesus never actually stated the quote you have. Jesus was a Jew. His message was for the Jews. So to call the Jews children of the devil would be counter productive. More so, it is only found in John, the Gospel that is the most anti-Jewish. Most scholars agree that that quote is the feeling of the community that produced the Gospel of John, probably because of their tension with the Jewish community).
Jesus died because he was a criminal. He went into the Temple, during Passover, and caused a massive scene and disturbance. That was a crime worthy of death.
As someone mentioned, it can also be argued that Jesus did in fact know he was going to be killed. It is actually logical as people in his position usually were killed by the Roman government. We can look at John the Baptist, who had an impact on the life of Jesus. He was killed for the same reason. And Jesus would have heard of others as well. The path he was on was one that would lead to death. It was only time before he caught the attention of the wrong person, and they had him killed. Jesus would most likely have known this.
Again though, the sacrifice didn't rely on those two ideas. As Storm said much better than I could, it was about a blood sacrifice.