A careful reading of the NT data shows why the Apocrypha must be rejected. Neither the Lord Jesus nor his Apostles ever quote from the Apocrypha as an inspired source of revelation.
Author G. Douglas Young asks:
In fact, the Lord Jesus himself confirms the three-fold division of the Old Testament, a division which, as we shall show, excluded the Apocrypha:
The mentioning of the prophets from Abel to Zechariah affirms that Jesus viewed the Jewish canon as inspired by God. This is based on the fact that the canon of the Jewish scriptures began/begins with Genesis (i.e. “the blood of Abel” - Genesis 4:3-11) and ends(ed) with Chronicles (i.e. “the blood of Zechariah” - 2 Chronicles 24:20-21). This again is an explicit testimony from the Lord Jesus Christ that the apocryphal writings have no place in the OT canon as Roger Beckwith, considered by many to be one of the leading authorities regarding the issue of the OT canon, explains:
Furthermore, Jesus and the NT writers implicitly affirm that for a book to be part of the OT canon it had to have been written during Israel’s prophetic period, i.e. during the time when there were prophets in Israel:
“Do not think that I have come to abolish the Law or THE PROPHETS; I have not come to abolish them but to fulfill them.” Matthew 5:17
“So in everything, do to others what you would have them do to you, for this sums up the Law AND THE PROPHETS." Matthew 7:12
“‘But this has all taken place that THE WRITINGS OF THE PROPHETS might be fulfilled.’ Then all the disciples deserted him and fled.” Matthew 26:56
“The Law AND THE PROPHETS were proclaimed until John. Since that time, the good news of the kingdom of God is being preached, and everyone is forcing his way into it.” Luke 16:16
“Abraham replied, ‘They have Moses and THE PROPHETS; let them listen to them.’ ‘No, father Abraham,’ he said, ‘but if someone from the dead goes to them, they will repent.’ He said to him, ‘If they do not listen to Moses and THE PROPHETS, they will not be convinced even if someone rises from the dead.’” Luke 16:29-31
“Jesus took the Twelve aside and told them, ‘We are going up to Jerusalem, and everything that is written BY THE PROPHETS about the Son of Man will be fulfilled.’” Luke 18:31
“He said to them, ‘How foolish you are, and how slow of heart to believe ALL THAT THE PROPHETS HAVE SPOKEN! Did not the Christ have to suffer these things and then enter his glory?’ And beginning with Moses AND ALL THE PROPHETS, he explained to them what was said IN ALL THE SCRIPTURES concerning himself.” Luke 24:25-27
“Philip found Nathanael and told him, ‘We have found the one Moses wrote about in the Law, and about whom THE PROPHETS ALSO WROTE – Jesus of Nazareth, the son of Joseph.’” John 1:45
"It is written IN THE PROPHETS: ‘They will all be taught by God.’ Everyone who listens to the Father and learns from him comes to me.” John 6:45
“Now, fellow Israelites, I know that you acted in ignorance, as did your leaders. But this is how God fulfilled what he had foretold through ALL THE PROPHETS, saying that his Messiah would suffer… For Moses said, ‘The Lord your God will raise up for you a prophet like me from among your own people; you must listen to everything he tells you. Anyone who does not listen to him will be completely cut off from among his people.’ Indeed, ALL THE PROPHETS from Samuel on, as many as have spoken, have foretold these days.” Acts 3:17-18, 22-24
“But God turned away and gave them over to the worship of the heavenly bodies. This agrees with what is written IN THE BOOK OF THE PROPHETS: ‘Did you bring me sacrifices and offerings forty years in the desert, O house of Israel?’” Acts 7:42
“ALL THE PROPHETS testify about him that everyone who believes in him receives forgiveness of sins through his name.” Acts 10:43
“After the reading from the Law AND THE PROPHETS, the synagogue rulers sent word to them, saying, ‘Brothers, if you have a message of encouragement for the people, please speak’… The people of Jerusalem and their rulers did not recognize Jesus, yet in condemning him they fulfilled the words of THE PROPHETS that are READ every Sabbath.” Acts 13:15, 27
“But I have had God's help to this very day, and so I stand here and testify to small and great alike. I am saying nothing beyond what THE PROPHETS and Moses said would happen…King Agrippa, do you believe THE PROPHETS? I know you do.” Acts 26:22, 27
“They arranged to meet Paul on a certain day, and came in even larger numbers to the place where he was staying. From morning till evening he explained and declared to them the kingdom of God and tried to convince them about Jesus from the Law of Moses and from THE PROPHETS.” Acts 28:23
“Paul, a servant of Christ Jesus, called to be an apostle and set apart for the gospel of God - the gospel he promised beforehand through HIS PROPHETS in the Holy Scriptures regarding his Son, who as to his human nature was a descendant of David, and who through the Spirit of holiness was declared with power to be the Son of God by his resurrection from the dead: Jesus Christ our Lord.” Romans 1:1-4
“But now a righteousness from God, apart from law, has been made known, to which the Law AND THE PROPHETS testify.” Romans 3:21
“Now to him who is able to establish you by my gospel and the proclamation of Jesus Christ, according to the revelation of the mystery hidden for long ages past, but now revealed and made known through the PROPHETIC WRITINGS by the command of the eternal God, so that all nations might believe and obey him–” Romans 16:25-26
“In the past God spoke to our forefathers THROUGH THE PROPHETS at many times and in various ways, but in these last days he has spoken to us by his Son, whom he appointed heir of all things, and through whom he made the universe." Hebrews 1:1-2
“Concerning this salvation, THE PROPHETS, who spoke of the grace that was to come to you, searched intently and with the greatest care, trying to find out the time and circumstances to which the Spirit of Christ in them was pointing when he predicted the sufferings of Christ and the glories that would follow. It was revealed to them that they were not serving themselves but you, when they spoke of the things that have now been told you by those who have preached the gospel to you by the Holy Spirit sent from heaven. Even angels long to look into these things.” 1 Peter 1:10-12
“And we have THE WORD OF THE PROPHETS made more certain, and you will do well to pay attention to it, as to a light shining in a dark place, until the day dawns and the morning star rises in your hearts. Above all, you must understand that no prophecy of Scripture came about by THE PROPHET’S own interpretation. For prophecy never had its origin in the will of man, but men spoke from God as they were carried along by the Holy Spirit.” 2 Peter 1:19-21
“I want you to recall the words spoken in the past BY THE HOLY PROPHETS and the command given by our Lord and Savior through your apostles.” 2 Peter 3:2
"But in the days when the seventh angel is about to sound his trumpet, the mystery of God will be accomplished, just as he announced TO HIS SERVANTS THE PROPHETS.” Revelation 10:7
Therefore, for the Apocrypha to be Scripture they must have been written at a time when God was still sending prophets to his people.