When Jesus quoted the bible did he quote the OT of the NT?
Obvious answer ,I know .
If Jesus did not need the NT why do we ?
First let us look at the Gospels.
These record events of Christ's ministry, and the quotes that you mentioned. So, we need the Gospels.
Acts of the Apostles tell the history of the work that Jesus commissioned them to do, and clearly shows his backing.
Now the letters.
The change from the Jewish system of hundreds of laws, and a physical temple with a priesthood, to a brotherhood of ministers, who all were assigned to share in the ministry was a major and new concept. All other faiths in the world at that time focused on the similar pattern that the Jews had.
How then did this brotherhood handle the change? The letters of Paul, Peter, John, Jude and James showed the different needs that this expanding congregation, tied by faith, and not by family or by nationality had to face and the counsel that this body of men gave to deal with them.
We see with Paul's letters the importance of the events recorded in the Hebrew scriptures, the pattern that was set in them to point to the Christ and his ministry.
(Acts 3:22-23)
22 In fact, Moses said, ‘Jehovah God will raise up for YOU from among YOUR brothers a prophet like me. YOU must listen to him according to all the things he speaks to YOU. 23 Indeed, any soul that does not listen to that Prophet will be completely destroyed from among the people.’
(2 Corinthians 3:7-11)
7 Moreover, if the code which administers death and which was engraved in letters in stones came about in a glory, so that the sons of Israel could not gaze intently at the face of Moses because of the glory of his face, [a glory] that was to be done away with, 8 why should not the administering of the spirit be much more with glory? 9 For if the code administering condemnation was glorious, much more does the administering of righteousness abound with glory. 10 In fact, even that which has once been made glorious has been stripped of glory in this respect, because of the glory that excels it. 11 For if that which was to be done away with was brought in with glory, much more would that which remains be with glory.
(Romans 10:5-10)
5 For Moses writes that the man that has done the righteousness of the Law will live by it. 6 But the righteousness resulting from faith speaks in this manner: “Do not say in your heart, ‘Who will ascend into heaven?’ that is, to bring Christ down; 7 or, ‘Who will descend into the abyss?’ that is, to bring Christ up from the dead.” 8 But what does it say? “The word is near you, in your own mouth and in your own heart”; that is, the “word” of faith, which we are preaching. 9 For if you publicly declare that ‘word in your own mouth,’ that Jesus is Lord, and exercise faith in your heart that God raised him up from the dead, you will be saved. 10 For with the heart one exercises faith for righteousness, but with the mouth one makes public declaration for salvation.
And then the book of Revelation.
John did not have much of a choice. He was given this revelation for the future generation that would be living in days of the Lord.
(Revelation 1:10,11)
10 By inspiration I came to be in the Lord’s day, and I heard behind me a strong voice like that of a trumpet, 11 saying: “What you see write in a scroll and send it to the seven congregations, in Eph?e?sus and in Smyr?na and in Per?ga?mum and in Thy?a?ti?ra and in Sar?dis and in Philadelphia and in La?o?di?ce?a.”
So, to be a Christian, we need all the writings that help us to deal with the same issues that faced the 1st Century congregation.