I believe Jesus was contrasting the need to eat His flesh and drink His blood, over and against pagan worship that you referenced.
Obviously as a Protestant I believe the blood and wine are symbolic, not actual. But I believe the point of this Bible passage is the contrast with the surrounding pagan worship.
Jesus ate the bread and wine at the Last Supper, as most have seen illustrated in the great painting by Da Vinci. He was physically present there, body and blood. No one there seemed to be under the impression that parts of His body or servings of His blood were being served as He Himself sat there and partook with them.
So did almost everyone else, until the Fourth Lateran Council, in 1215, invented the notion of transubstantiation out of whole cloth.
The doctrine of the Eucharist that was accepted semper, ubique, et ab omnibus, is that of the Real Presence.