Whenever we read the Bible, we have to read it in context. We cannot anachronistically superimpose our own Christian doctrine on it and then say that it is true.
The verse you are speaking about, Matt. 6:33, comes from the book of Matthew. The book focuses on the Messianic Character of Yeshua, and in it, Yeshua is addressing Jews for there were no Christians yet.
The Kingdom of God concept that he refers to comes out of his declaration to Israel that he had come to bring in the Year of Jubilee that God promised them while they were in exile.
Yeshua says here that whatever you think you need is not as important as seeking God’s Kingdom on Earth. That is what Yeshua came to bring. (Luke 4:18)(Isaiah 61:1-3)
Yeshua demonstrates that Kingdom in all his miracle-working. It is being initiated in his life, death and resurrection. That was the time that the Gentiles would be allowed into the covenant that God was renewing with Israel as outlined in Jeremiah 33, during the Babylonian exile. God always intended to restore His people (Israel). They, the people of Israel, do not have to be saved to be in relation to Him, their covenant with Him does that. His covenant is eternally binding, on Him. Yeshua was bringing in the Eschaton, or so says Paul in most of his Epistles. It was good news for Israel as well as the Gentiles. Israel’s God was coming to His people, and as promised, He would begin the ingathering of the Gentiles as well. The point in the Matthew passage is that the people’s hearts should have focused on what God was doing on Earth, as God’s Kingdom was being realized. They were not to focus on themselves. God had, and would always take care of His people.