There is no doubt 2022 was a good year from Perez's perspective after he picked up two race wins and finished third in the Drivers' Championship - his best Formula 1 campaign to date.
However, the pressure to perform at Red Bull is immense and Fernandez believes Checo needs to step it up a gear this season.
For example, his teammate Max Verstappen broke multiple records enroute to winning the Drivers' Championship for the second year in a row.
"Checo is performing well," Fernandez told the Dutch edition of Motorsport.com.
"The problem is that Verstappen is driving next to him.
"Checo is an excellent driver and now very experienced. But now he has to find out what Max does differently from him.
"Max has of course been driving for Red Bull for some time and the team is built around him. Considering that, Checo is certainly not doing wrong and is probably doing exactly what the team wants him to do.
"But he will soon have to step up a gear. And I think he knows that too.
"Red Bull was very strong last year, but if the competition is closer next season, it will be even more important for the team to have two drivers at the front.
"Max is just on a different level," Fernandez continued.
"He is of the calibre of Senna, Schumacher and Hamilton.
"I believe in Checo's ability, but to get to that level, he will have to take a big step.
"And I'm not so much talking about how he drives, but more about how he works with the engineers to get the car to his liking and his consistency throughout the season.
"Being fastest over a lap once, finishing a session on top or winning a race, it's all well and good but if you're going for the championship you're going to have to be strong all season.
"Look at Valtteri Bottas. He spent years in the best car, but failed to become champion. The difference between him and Lewis? Consistency. That is what makes champions so special."