But not necessarily measuring up to their standards, because they didn't like what he said. Seeing the hardness of hearts of the Jewish leaders, he decided to prophecy against them. Several times in fact.
You can tell from Jesus's words against the Canaanite woman, about how he came for the Jews, and it is "not right to take the children's bread, and feed it to the dogs." Yet her response clearly changed his view on who was deserving of his ministry. After this, he preached on the Good Samaritan, and generally seemed more about saving the Christians than reforming the Jews. The sinners among the Jews were another story, but he largely stopped trying with the Pharisees, Saducees, and scribes.
There is no prophecy of a Gentile Messiah, this is true. But the Messiah decided the Jews weren't ready yet. So, while among the early Christians, they were mostly circumcised Jews to start with, we have Peter's vision, and afterwards, non-Jews are being converted.