Yes, you are right.
Judea/Israel was under Roman rule in 33AD. The Jews and Chief/High Priest had no legal authority to put offending Jews or anyone to death, eg for breaking Moses Law - adultery, homosexuality, incest, blasphemy, idolatry, etc - these were instead permitted under Roman Law. The Jews and Chief Priest wanted to get rid of Jesus because they desired for a Christ/Messiah who would militarily defeat the Romans and gift them back their kingdom of earth, ie Judea/Israel.(JOHN.6:15)
....... To get the Roman ruling authorities to crucify Jesus Christ, they made false accusations against Him as being a rebel "King of the Jews". Pontius Pilate was not convinced but had to acquiesce to them when a Jewish mob/riot threatened.
After "killing/murdering" Jesus Christ, they followed-up by persecuting His followers as Jewish heretics/cult, eg the first Jewish Christian martyr, Stephen, at ACTS.7.
....... They even appointed false christs to lead them into armed rebellion against the Romans = the Jewish-Roman Wars - MATTHEW.24:15 & 24, LUKE.21:20.
As per ROMANS.12:19-21, God's vengeance upon the Jews and Chief Priest for "murdering" His Son occured in 70AD when a mighty Roman Army arrived in Judea/Israel to squash the Jewish rebellion = the Jews were massacred and their Holy Temple of God in Jerusalem destroyed. Thereafter, no Jews were allowed to settle in Judea/Israel = became back to Palestine/Philistine.