Jesus does make the distinction that you point out, but he is not making the distinction between Himself and God; He is differentiating between Himself (Son) and the Father. To be fair, I can understand why your knowledge of the Bible may be incomplete since it is no longer your sacred text. So, let’s look at a fuller picture of what Jesus is saying.
As we read the gospels, we find Jesus saying something new about God–there are hints and foreshadowings of it in the Old Testament, but certainly no statement. Alongside his insistence that God is one, there is a continual reference to some sort of plurality. There is no watering-down of the strictest monotheism–Jesus quotes from the Old Testament: “Hear O Israel, the Lord thy God is one God.” But there is a new element of more-than-oneness, which still leaves the oneness perfect.
Matthew (11:27) and Luke (10:22) give us one phrase: “No one knows the Son but the Father; and no one knows the Father but the Son.” Here are two persons put on the same level. “I and the Father are one” (Jn 10:30). They are two persons, yet one.
At the very end of Matthew’s Gospel, a third is brought in, still within the oneness–“Baptizing them in the name of the Father, and of the Son, and of the Holy spirit”–three persons, but with the one name, and therefore one nature, since God names things for what they are.
What is especially to be noticed is a kind of “interchangeableness.” When Phillip the Apostle says, “Let us see the Father,” Jesus answers, “Whoever has seen me has seen the Father.” Similarly, Jesus says that he will answer our prayer (Jn 14:14) and that his Father will (Jn 16:23), that he will send the Holy Spirit (Jn 16:7) and that his Father will (Jn 14:16).
In the doctrine of the Trinity, all these phrases fall into place.