The Malaysian entrepreneur, who also runs Queens Park Rangers soccer club and the AirAsia airline, told reporters at the Caterham factory that there would be no point carrying on if the team remained uncompetitive.
"If we are at the back, I don't think we're going to carry on," he said.
"After five years and to get no points, there's a limit to everyone's patience, money etc," added Fernandes, who will have two new drivers this year in Japan's Kamui Kobayashi and Sweden's Marcus Ericsson.
Caterham came into the sport as Lotus Racing with two other new teams in 2010 when a budget cap was talked about and then abandoned. None have scored points in four seasons and Spanish-based HRT folded at the end of 2012.
Last year, Caterham finished last of the 11 Formula One teams while QPR were relegated from the Premier League.
Fernandes compared Formula One unfavourably to football, saying it was too predictable, too expensive, not exciting enough and with insufficient chances for underdogs to create an upset.
"The sport has to examine itself," he declared.
"I think if we are going to every race and are not competing, two seconds behind everyone else, then we haven't made any progress," added the Malaysian, a fervent believer in the need for a cost cap.
"If we are not competing then we have got to seriously examine ourselves as to whether this makes sense."
Fernandes said however that his words were not to be taken as an ultimatum and he was making a statement of intent because he believed Caterham would make the required progress at a time of huge technical change.
"I am saying these things with the confidence that I think we will deliver," he said. "I would not be here otherwise. But I am also being real that if we don't...I don't think anyone in this office expects us to carry on being last.
"But we are fairly confident that we should see some progress."
The sport is introducing a new V6 turbocharged engine this season, replacing the old V8, and reliability is a major concern - opening up the possibility that smaller teams could score points if others suffer failures.
"Me walking away would make a fairly large dent to the team, without sounding egotistical," Fernandes said of the impact his departure would have.
Asked whether he could also walk away from QPR if they failed to secure a quick return to the Premier League from the Championship (second tier), he shook his head. "No, because we are making progress. Even if we don't go up this season, we have made good progress.
"We have got to see progress. It's the same for AirAsia. If AirAsia was still a two plane operation and losing tons of money every year, you'd have to say 'Er, what's the point of carrying on guys?'."
(Reporting by Alan Baldwin, editing by Justin Palmer)
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