And the actual context of the passage indicates otherwise.
52Then the Jews began to argue with one another, saying, How can this man give us His flesh to eat? 53So Jesus said to them, Truly, truly, I say to you, unless you eat the flesh of the Son of Man and drink His blood, you have no life in yourselves. 54He who eats My flesh and drinks My blood has eternal life, and I will raise him up on the last day. 55For My flesh is true food, and My blood is true drink. 56He who eats My flesh and drinks My blood abides in Me, and I in him. 57As the living Father sent Me, and I live because of the Father, so he who eats Me, he also will live because of Me. 58This is the bread which came down out of heaven; not as the fathers ate and died; he who eats this bread will live forever.
59These things He said in the synagogue as He taught in Capernaum.
60Therefore many of His disciples, when they heard this said, This is a difficult statement; who can listen to it? 61But Jesus, conscious that His disciples grumbled at this, said to them, Does this cause you to stumble? 62What then if you see the Son of Man ascending to where He was before? 63It is the Spirit who gives life; the flesh profits nothing; the words that I have spoken to you are spirit and are life.
64But there are some of you who do not believe. For Jesus knew from the beginning who they were who did not believe, and who it was that would betray Him. 65And He was saying, For this reason I have said to you, that no one can come to Me unless it has been granted him from the Father.
66As a result of this many of His disciples withdrew and were not walking with Him anymore. 67So Jesus said to the twelve, You do not want to go away also, do you? 68Simon Peter answered Him, Lord, to whom shall we go? You have words of eternal life. 69We have believed and have come to know that You are the Holy One of God.
And yet; Jesus did NOT offer the disciples any little bits and pieces of flesh and flakes of blood that still were on His body when He appeared in their midst.
Don't worry; there's more where this came from.