The blood curse refers to a New Testament passage from the Gospel of Matthew, which describes events taking place in Pilate's court before the crucifixion of Jesus and specifically the apparent willingness of the Jews to accept liability for Jesus' death.
Matthew 27:24-25 reads:
So when Pilate saw that he was gaining nothing, but rather that a riot was beginning, he took water and washed his hands before the crowd, saying "I am innocent of this man's blood; see to it yourselves." And all the people answered, "His blood be on us and on our children!" (Greek: ? ' ? ?)
This passage has no counterpart in the other Gospels and is probably related to the destruction of Jerusalem in the year 70 CE. German Protestant theologian Ulrich Luz (b. 1938) describes it as "redactional fiction" invented by the author of the Matthew Gospel. Some writers, viewing it as part of Matthew's anti-Jewish polemic, see in it the seeds of later Christian antisemitism. In the view of the late Graham Stanton, a British New Testament scholar in the Reformed tradition, "Matthew's anti-Jewish polemic should be seen as part of the self-definition of the Christian minority which is acutely aware of the rejection and hostility of its 'mother' Judaism." Howard Clark Kee has written, "The bitter words he [Matthew] attributes to the Jews have caused endless harm in arrousing anti-Jewish emotions."Donald A. Hagner, a Presbyterian New Testament scholar and theologian, has written, "It cannot be denied that this statement, unfortunately, has been used to promote anti-Semitism. The statement is formulaic, and the reference to 'our children' does not make them guilty of the death of Jesus, let alone children or Jews of later generations."
N.T. Wright, an Anglican New Testament scholar and theologian, has stated, "The tragic and horrible later use of Mt. 27.25 ('his blood be on us, and on our children') as an excuse for soi-disant 'Christian' anti-semitism is a gross distortion of its original meaning, where the reference is surely to the fall of Jerusalem."
Anglican theologian Rowan Williams, then Archbishop of Wales, and who would soon become Archbishop of Canterbury, has written of Matthew's Gospel being made "the tool of the most corrupt and murderous misreading of the passion stories that has disfigured the Church's record."
"The evangelist's bitterness at the schism within God's people that continues in his own day, his impatience with the refusal of the Jewish majority to accept the preaching of Jesus, overflows into this symbolic self-denunciation by 'the people'. It is all too likely that his first readers heard it as a corporate acknowledgement of guilt by the Jewish nation, and that they connected it, as do other New Testament writers, with the devastation of the nation and its sacred place in the terrible disasters of AD 70, when the Romans destroyed the Temple and along with it the last vestiges of independent power for the people. Read at this level, it can only make the contemporary Christian think of all the centuries in which Jewish guilt formed so significant a part of Christian self-understanding, and of the nightmare which was made possible by this in the twentieth century."
Pope Benedict XVI writes of this incident:
"When in Matthew's account the "whole people" say: "His blood be upon us and on our children" (27:25), the Christian will remember that Jesus' blood speaks a different language from the blood of Abel : it does not cry out for vengeance and punishment; it brings reconciliation. It is not poured out against anyone; it is poured out for many, for all." 
St. John Chrysostom wrote of this incident:
"Observe here the infatuation of the Jews; their headlong haste, and destructive passions will not let them see what they ought to see, and they curse themselves, saying, "His blood be upon us," and even entail the curse upon their children. Yet a merciful God did not ratify this sentence, but accepted such of them and of their children as repented; for Paul was of them, and many thousands of those who in Jerusalem believed".