God has not contradicted Himself. In Deuteronomy He is speaking of animal sacrifice for the sins of the people. He says clearly that it is the blood that gives life so they are not to eat of the blood of animals.
Jesus is not some animal. He is God. His blood gives the life that is eternal. He says exactly that in John.
There is a huge difference between partaking of the lifeblood of animals and that of the life giving blood of God.