Why not? God did the preposterous act of taking human flesh, being born, allowing Himself to be crucified and die. That is also human sacrifice, in this case of the God-Man.
The Eucharistic doctrines of the Catholic Church are not more preposterous than the Incarnation itself. If you cannot believe in the Real Presence, its difficult to see how you can truly believe God became man.
Second. He sent His Son Jesus, God incarnate... This is the Mystery. How can a young girl be impregnated with out having sex...Well, God designed the body, He can modify it anyway he sees fit for His Glory. Though God manifested himself in Man, he did that for the remission of sins. Jesus dying on the cross was the final sacrifice. No more sacrifices are needed to attone for man's sins.
No other sacrifice was good enough for God. Therefore, He had to send Jesus for that purpose. As for the Eucharist... Man made items will not be good enough for God to manifest himself. God only manifested himself in the Holy of Holies... not in a wafer. The Holy of Holies wasn't to be entered into by man unless he was Chosen by God to enter. God will not allow his son to be "crucified" again.