Jesus made some bold claims on how he is the bread of life and how his flesh is his food. For the audience (who thought literally), such sayings seemed hard!
In response to the questions-now-complaints, Jesus talked about how he would later ascend. He also talked about how the Spirit gives life while the flesh doesn't, and that his words were powered by the Spirit (6:63).
However, most notably, Jesus revealed how some of the Judeans still did not believe in Jesus (6:64). He knew the unbelievers and betrayers (those who would leave Jesus) right from the start -- at least the start of the entire conversation (6:65). It's likely that Jesus knew the hearts and attitudes of the Judean audience. From 6:15, the Judeans expected Jesus to be like a king (at least in their view), and someone who seems to give up themselves doesn't seem to fit the role for them.
Finally, Jesus talks about how people could not come to Jesus (he means in a spiritual sense rather than physical location) "unless it has been granted [...] by My Father" (6:65). Based on prior passages regarding belief and coming to Jesus, we know that the Father grants those who are willing to come to him. Not to mention that it takes God's work for us to even understand him.