Countless times Jesus cited the Law and the Prophets as His authority. I do not recall any instance where He said, "Verily, verily, I say unto you . . . . because verily, verily I have said it." Likewise the Aposltes, particular Paul, peter, and John who wrote the majority of the epistles, are extremely liberal in their citations from the Law and the Prophets concerning their teachings. The only exception might be in I Corinthians where Paul definitely tells his readers that it is his opinion, not the Lord's.
The RCC, by contrast, has evolved its own Tradition which it uses to buttress various dogmas and doctrines which are unique to its Tradition. Papal infallibility happens to be one of those.