Christ's church? or the Roman Catholic church? Two different entities. Anyway, since you asked, let us look at the context. And in order to do it we must go back a few verses. Was Jesus or was he not speaking of the Lord's Supper?
v26-27 Jesus knows the people followed him to get something to eat. He tells them to work for the meat which does not perish. Meat? Hey, I thought we were talking about bread?? Well, the point is "that which provides nourishment."
v28 the people ask what they should do. Note they didn't say what they should eat. They understood him (at THAT point) to be talking about doing the works of God. Clear evidence they understood him at that point as speaking of working the works of God
v29 Jesus replies that they must believe on Him whom God sent
v30-31 They ask him for a sign that he is from God and pull up as an example that Moses gave them manna in the wilderness.
v32 Jesus corrects them in saying that it was not Moses, but God which gave them that manna
v33. Jesus then draws a comparison using their own example, that just as God sent the manna to sustain Israel, the Son of Man sustains mankind, and gives us life. Note: so far we have no mention of the Lord's supper or "Holy Communion".
v34 This is where they really get tripped up. They are expecting more manna-style feeding. This is why they said "evermore" give us this bread. Manna at one point ended, but these Jews wanted whatever bread they thought Jesus was talking about to last forever.
v35 Jesus says that he is the bread of life. That is, he is God's gift to us, that sustains us. Notice he says the words "cometh" and "believeth", and no mention or even anything that would remotely lead you to communion.
v36-42 Jesus continues teaching about the bread of life. Notice that he has not yet said anything about eating his flesh, yet in verse 42 is where the Jews are first offended at his teaching. They can't understand how he can be the bread of life. They are looking for a physical bread to eat, and it is plain that Jesus is in no wise talking about a physical bread at all, whether at a communion table or otherwise. It's called a metaphor if you care to hear it.
v43-47 Jesus goes into more teaching about coming to him, being taught of God, etc.
v48 Reasserts that he is the Bread of Life
v49 Jesus makes a comparison - notice that the people who ate the physical bread are now dead.
v50-52 Now he speaks of his death on the cross as being that which will be the source of life for the world. Now the Jews are really stuck on that physical bread, just as the Catholics are stuck on the very same teachings of Jesus today. It is not physical bread or communion that Jesus refers to. It is not the context of the passage.
v53-54 Jesus teaches that we need to make his teachings a part of our life. This is what the metaphor boils down to. We must pattern our lifes, our actions, after him.
55-56 He is saying here that the true source for life eternal is Himself and no other.
v57-58 Jesus even goes to the trouble of drawing a contrast between the physical and spiritual bread. IE this is not bread that you can physically eat.
v59 He taught these things in Capernaum
v60 Some disciples fell away and said "This is a hard saying. Who can hear (understand) it? Lots of people are still doing this today
So there you have it. It's all about context. Jesus was not teaching anything about transsubstantiation in this passage. If he was, the apostles would have understood it, at the very least after the Day of Pentecost, and would have taught it to the church. They did not teach it to the church. Were they wrong?