I would refer you to the Letter of St. Clement to the Corinthians. St. Clement was the third successor to St. Peter of the See of Rome. He was a companion to St. Paul (Phil 4:3) and would have learned from him. In his letter, he uses selections from both the Old and New Testaments. He quotes Genesis, Ephesians, First and Second Peter, Acts, Titus, Proverbs, Deuteronomy, First and Second Corinthians, Wisdom, Exodus, Numbers, First Kings, all four Gospels, Ezekiel, Isaiah, Hebrews, Romans, Second Chronicles, Judith, James, Joshua, Jerimiah, Proverbs, Psalms, Job, Numbers, Habakkuk, Malachi, Daniel, and Esther. Thirty four books, 14 from the New Testament: not a bad list.
The fact that he does not directly say, “this is from the Gospel of Matthew” (for example) does not particularly bother me. He used the reference; he would have known the entire book to take the reference from.