Many Catholics seem to have picked up on the significance that all of the action in John 6 takes place in a 24-hour period. John 6:1-15, Loaves and Fishes, takes place during the day. John 6:16-21, Jesus Walking on Water, takes place that evening, and is due to Him withdrawing from the people (who want to make Him a human ATM/vending machine and secular king). John 6:22-71, the Bread of Life discourse, begins the next day, and significantly, is to the same crowd as who received the loaves and fishes.
The Bread of Life discourse is very Eucharistic:
Whoever eats* my flesh and drinks my blood has eternal life, and I will raise him on the last day. For my flesh is true food, and my blood is true drink. Whoever eats my flesh and drinks my blood remains in me and I in him.
The NAB footnote mentions that the term used isn't the normal word for eating, but means more literally "munch" or "gnaw," and is hyper-literal. Jesus used a term which wasn't a common metaphorical term, seemingly to dispel any notion He was speaking anything but literally. In any case, the crowd initially (John 6:34) has trouble understanding that He's not talking about bread or manna in the way He had been yesterday, but that He means spiritual Bread. When they grasp this, they think (John 6:41-42) He's just saying that He's come down from Heaven; in other words, they take a metaphoric interpretation. Then, they get it (finally -- John 6:52). While He re-explains past their confusion the first two times, He does not do so the third [precisely because there was no confusion]. At that point, a lot of them freak out (John 6:60) and bail out (John 6:66). Jesus still doesn't let up, presenting the Eucharist as a sort of ultimatum even to the Apostles (John 6:67), although Peter meets the challenge (John 6:68-69).
So what was the important and easy-to-miss detail in all of this? It's back at the start of the chapter, in the loaves and fishes account. Specifically, John 6:3-4
Jesus went up on the mountain, and there he sat down with his disciples. The Jewish feast of Passover was near.
"The mountain" has really important symbolism almost every time it's mentioned. It's a spot of teaching, and it's where the Law came down from God in Exodus. It signifies both that Jesus is the Word Incarnate, and that He is a great teacher (hence the "Sermon on the Mount"). But more importantly for our purposes, John's Eucharistic discourse, like the other three, takes place at Passover-time -- the Eucharist and the Passion are forever and inseparably linked.
So yeah, John does introduce the Eucharist; he just does it a year earlier than the Synoptics.