It's always been understood that the jews orchestrated it but in typical jew fashion, they got someone else to do their dirty work. So the Romans carried out the act but when people try to solely put responsibility on them, it's because they've been subjected to years of programming that won't allow them to put the blame on jews for ANYTHING in world history, even if there's overwhelming evidence of their guilt. In the Gospel accounts, Pilate makes it clear that he finds no guilt in Christ, but he ignores his conscience to do what was expedient for him in order to appease the jews so they would stop whining. (It didn't work.)
Their motive was that Christ (God in flesh) didn't fit their preference for a Messiah. They wanted him to be a political messiah and Jesus didn't fit that mold so they killed him. "Let his blood be upon us and upon our children." Can't be much clearer than that. The Church Fathers and early saints all put the blame on them. St. Paul says so in the letters to the Thessalonians. St. Augustine wrote "The true image of the Hebrew is Judas Iscariot who sells the Lord for silver. The Jews can never understand the scriptures, and forever bear the guilt of the death of Christ." St. John Chrysostom has a whole collection of homilies called "Adversos Judaeos" (Against the Jews) that have some pretty harsh things to say about them. St. Gregory of Nyssa called them "assassins of the Prophets, companions of the Devil, a race of vipers, a Sanhedrin of Demons, enemies of all that is beautiful, hogs and goats in their lewd grossness." The list goes on. This "the Romans did it" nonsense is a more recent subversion of the traditional understanding of the Passion.
