Pilate had his hand tied at the time. His good friend had just been tired and executed for treason and now Pilate was being watched very closely. He had to keep a riot from happening at all costs, or it wouldโve been interpreted as him trying to start trouble for Rome in his province. He really didnโt want to kill Jesus, but he wasnโt going to want to stick his neck out too far since he was on a knifeโs edge himself. Iโm sure God wouldโve had mercy on him given his difficult situation and the fact he actually tried to get Jesus set free. The only ones who are sole to blame for Jesusโ death are the Jews. Of course though, Jesus had to die that we may be redeemed. But the Jews are still the ones responsible for it.
