Jesus came to the Jews to preach the Gospel,and the New Testament,and He only referred to the Old Testament because they were still under the Old Testament,but His main goal was for them to accept Him,which is the Gospel,which John prepared the way for Jesus to get the nation of Israel ready for His arrival.
John was preaching Jesus before He started His ministry,so surely Jesus would of preached the acceptance of Him to the Jews,which is the Gospel.
Mar 1:1 The beginning of the gospel of Jesus Christ, the Son of God;
Mar 1:2 As it is written in the prophets, Behold, I send my messenger before thy face, which shall prepare thy way before thee.
Mar 1:3 The voice of one crying in the wilderness, Prepare ye the way of the Lord, make his paths straight.
Mar 1:4 John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.
Mar 1:14 Now after that John was put in prison, Jesus came into Galilee, preaching the gospel of the kingdom of God,
Mar 1:15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
None of the teachings were only applicable to the Jews,for it is the Gospel that is for the whole world.Jesus might tell them to do something according to the Old Testament for they were still under the Old Testament,but they were to accept Him,the Gospel.That is all Jesus came to do is preach the Gospel.