That's not what you said. You blamed the Jews for killing Jesus. All the Jews. The Pharisee priests were not all the Jews, and they weren't even a majority of the Jews. You extrapolated this fact to blame all Jews everywhere
Not when it came to capital punishment. Only the Roman governor of Palestine had the authority to order executions for criminal or political offenses. The high priests wouldn't have even bothered to go to the Roman authorities if they could have just executed Jesus themselves.
John is the least reliable of the gospels as historical source material, because it was written significantly after the synoptic gospels and seems to have been primarily concerned with a theological agenda.
The earliest Gospel, Mark, which is probably based directly on the eyewitness of Peter, makes it clear Pontius Pilate ordered the executions, although the high priests seem to have collaborated to bring Jesus to the Roman authorities. An independent corroborating source is the Jewish historian Josephus who makes crystal clear that Pontius Pilate was a ruthless provincial governor who would quickly execute anyone perceived to be stirring up trouble.
Overall, there is a tendency in the gospels to blame the Jews for the demise of Jesus. But the bottom line is that no author of the gospels was going to openly write down that the Roman authorities were uniquely responsible for executing a righteous man, because that would have been a dangerous thing to do given that these authors lived under the jurisdiction of the empire.
