The need for 'sacrifice' is present in Hinduism too. It is however about individuals sacrificing their personal desires and needs.
Every time a person went on a pilgrimage (taking several weeks or months those days)...he or she was expected to give up something, it could be his favorite dish, special piece of clothing or anything that required will power. Some people would give up sleeping on a mattress, footwear, sex or something else.
Sacrifice was a way of self discipline and personal self control. By and by people started making it easier on themselves by sacrificing (killing) some animal or bird (and eating it later).
How the idea of God sacrificing his son came about in Christianity, is a different matter, I guess.