"I would say it's the media, the media's fault, because they're not getting my name out there," Rice told sportscaster Pete Liebengood during the interview at San Francisco International Airport.
"I don't know if I'll get any recognition in commercials or anything, but right now, the way things are looking, I'm not going to get nothing out of being MVP. Just the name, the MVP, and that's it."
San Francisco Chronicle sports editor John Curley said he was "taken by surprise" by the remark.
"If there's something we haven't said, if there's something he'd like to tell us, heck, he could have a byline story in the Chronicle anytime he wants," Curley said.
Glenn Schwarz, sports editor of the San Francisco Examiner, said: "I'm sorry he feels that way, because there was no conscious decision on our part to slight him."
Schwarz called Rice "a fantastic player" who has been featured prominently in the newspaper.
Rice said he is not asking "for all the recognition." But he claimed that if the MVP award had gone to Montana, the quarterback would have received more prominent coverage.
"If it were Joe Montana, Dwight Clark, it would have been headlines all over," Rice said.
"And, no, I'm not saying it's racism or nothing like that; I'm really just speaking from my heart. And I think everybody in the Bay Area would feel the same way."
Rice is black, Montana white.
When Liebengood asked whether Rice would agree that "there is an implication" of racism in his statement, Rice replied, "Yeah, I would say so."