Just like when people sinned in the Old Covnant they brought their sacrifices to the tabernacle and their sins were forgiven. This had to be done over and over again everytime some one sinned. Jesus was the last sacrifice, (Isaiah 53),now all we have to do is go to God directly and ask for forgiveness based on Jesus' once of all time sacrifice for us. So the prophecy is completely accurate concerning Jesus, He puts an end to sin in us, we are no longer condemned for it. He made atonement for iniquity. Animal sacrifice was no longer necessary and that is why God permitted the destruction of the second temple.