They assigned more and more blame to Jews. Notice that by the time the Gospel of John is written that Pontius Pilate is a sympathetic figure who believes Jesus is innocent but forced to acquiesce to the demands of a Jewish mob, which is a portrait that doesn't mesh with the historical picture of Pilate at all.
They rectified it by making him a Saint, of course. Around the 4th Century, Pilate was depicted artistically next to Daniel, who also protested the innocence of a person accused by Jewish elders. He was also depicted as washing his hands near other cleansing images, such as Jesus washing feet, baptism, etc. Augustine saw him as a reluctant instrument of God.
http://www.basarchive.org/sample/bswbBrowse.asp?PubID=BSBR&Volume=19&Issue=6&ArticleID=2
Why didn't the Roman Empire accept Judaism?