Fernandes has been part of the team since its foundation as Lotus in 2010 but the squad has yet to score a point in four seasons of racing.
Caterham slipped to 11th in the championship in 2013, having finished in 10th place throughout their first three campaigns.
Caterham announced on Tuesday that Kamui Kobayashi and Marcus Ericsson will race for the team in 2014 and Fernandes believes that this season is the opportune moment for them to progress.
"This is it - the final chance. We've given you the best infrastructure, the best potential drivers, but it is now down to all of you to go and do it," Fernandes said during Caterham's 2014 launch at the team's Leafield factory.
"If we're at the back, I don't think we're going to carry on. But after five years and no points; there's a limit to everyone's patience, money, etc. And the sport has to examine itself. I'll always talk directly and always say what I believe, but I'm in a fantastic position to see two sports: football and Formula One."
Fernandes was referring to his position as chairman of Queens Park Rangers, currently playing in England's Championship league.
"Every week I go to a game nervous as hell, whether I'm playing Yeovil, Doncaster or Leicester. Football is unpredictable. It's no secret that every year people are paying more money to watch football, TV rights are growing, global audiences are growing. What are they doing right that we're not doing right [in F1]?"
"We spend all our time on how long the pipe is, pr how good KERS is, but the racing stays the same. The three or four teams are there every week winning, there's no underdog that comes in."
Fernandes nonetheless believes that Caterham can make progress this season.
"I'm saying these things with the confidence that we will deliver, I wouldn't be here otherwise."
"But I'm also being real that if we don't then I don't think anyone in this office expects us to carry on being last. We're fairly confident that we should see some progress."
"2013 was a tough season – we knew it would be hard and we took a gamble which, ultimately, did not pay off, but nobody’s heads dropped, every single person in the team is working harder than ever to come back fighting, and I believe that this year we have our best ever chance of surprising a few people."
Fernandes also confirmed that team has struck a deal to use Toyota's windtunnel in Cologne this year.