Christ referred to the Old Testament Scriptures because He was addressing the Jews... to whom the law was given. The gentiles were NEVER given the law and were/ are not expected to follow the written law. That is called legalism and is expressly condemned by the Apostles, most notably, Paul. If you try to follow even one law, you are responsible to follow the whole law..., all 413 of them! If we took a look at your life, I wonder how many you break on any given day.
Galatians 5:1It is for freedom that Christ has set us free. Stand firm, then, and do not let yourselves be burdened again by a yoke of slavery.
2Mark my words! I, Paul, tell you that if you let yourselves be circumcised, Christ will be of no value to you at all. 3Again I declare to every man who lets himself be circumcised that he is obligated to obey the whole law. 4You who are trying to be justified by the law have been alienated from Christ; you have fallen away from grace. 5For through the Spirit we eagerly await by faith the righteousness for which we hope. 6For in Christ Jesus neither circumcision nor uncircumcision has any value. The only thing that counts is faith expressing itself through love.
7You were running a good race. Who cut in on you to keep you from obeying the truth? 8That kind of persuasion does not come from the one who calls you. 9“A little yeast works through the whole batch of dough.” 10I am confident in the Lord that you will take no other view. The one who is throwing you into confusion, whoever that may be, will have to pay the penalty. 11Brothers and sisters, if I am still preaching circumcision, why am I still being persecuted? In that case the offense of the cross has been abolished. 12As for those agitators, I wish they would go the whole way and emasculate themselves!
Did the first century Church have a Bible, of course not. They had the letters of Paul and the other Apostles... that's it. They didn't follow the law, because Paul told them not to. So how do you explain that? If you were to say that that was necessary back then but we have the book now, I would say that that is a step backward, not forward.
Read the book of Galatians, you will find it quite liberating. The bottom line... if you try to be justified by the law, you are cut off from Christ! Jesus Christ is the "head of the Body". Does your body obey anything other that your head... I think not. If it does, you have some real issues going on. Neither does the Body of Christ. We obey the head because He leads us... directly, without the written word and without some "man of God" telling us what to do.