The 27 books of the Christian New Testament canon were not finalized until 367 CE.
Clement and Justin Martyr lived about 200 years before then.
The books of Revelation and 2 Peter were unheard of in their time, while the Apocalypse of Peter and the Shepherd of Hermas were read almost universally before then.
The idea of a Biblical canon was unknown in the time of Justin. It was a new invention of a contemporary heretic of his, Marcion of Sinope, a bishop that was excommunicated for his suggesting that the church should limit itself to doctrine based on a closed canon of texts and that the texts could produce salvific knowledge.
Due to the rise of the Marcionist threat, the church had to counter with its own canon. But prior to this, Christianity was based on the teachings from a "college" that passed down tradition learned from the Apostles. At one time the college was made up of Clement and Justin, who are known as the Church Fathers.
This is why Western schools of higher learning are called a "college" as opposed to a "yeshiva." Colleges are higher schools of learning once set up by Christians where you learned from the Elders or Fathers as opposed to yeshivas which are academies where Jews learn from rabbis.
This is why Jehovah's Witnesses are against sending their children to schools of higher learning. The foundation of such institutions are religious in nature, even though today one tends to associate then with the secular.
Oxford, Nortre Dame, Stanford, Yale--all these and more are all founded as religious universities. The Apostolic College, as it is known, passed its Tradition to the Church Fathers like Clement and Justin Martyr. Only later did they add a closed canon of Scriptures to Apostolic Tradition, but only by the authority already present in bishops passed down from and by the Fathers.