If my history is correct, Rav Natan lived before the Bavli was compiled. It seems that in a sense, Avot D'Rav Natan is a type of "tosefta". There are numerous midrashim and quotations in the Gemarrah that are duplicated in Avot D'Rav Natan. I would think the Gemarrah wouls cross reference the source in some way, but I haven't noticed it. At least, perhaps the Gemarrah would use a phrase like "Ta Shma" or "Amar Rav Natan" or something like that. Am I missing something in the lack of the Gemarrah's cross reference?
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The end of Maseches Horiyos records the story that Rebbe Meir and Rebbi Nosson attempted to oust Rabban Shimon Ben Gamliel from his position of Nasi. After they failed, Rabban Shimon "fined" Rebbi Nosson that his name should not be mentioned any more in the beis medrash. Therefore, his opinion is cited as "יש אומרים" - "some say."
For the same reason, it is possible that his Aggadic teachings were not referenced by name when quoted in the Talmud.
Avot deRabbi Natan was actually compiled in the Geonic era, as a sort of gemara on Pirkei Avot:
If so, it is quite probable that much of the material there which also appears in the gemara was actually drawn from the gemara. If so, we would not expect the gemara to reference Avot deRabbi Natan in any of those instances.