Belgium international Courtois, 22, got the nod to start the season after returning to Stamford Bridge from a loan spell with La Liga champions Atletico Madrid and helped Chelsea beat Burnley 3-1 at Turf Moor in their opening game.
“He is not my first choice for the rest of the season,” said Mourinho.
“He was my first choice today and he played well enough to be first choice for the next game. But when you have on your side a top professional like Petr and you don’t perform you are in trouble.
I’m not in trouble and Chelsea are not in trouble. They are safe because they are both fantastic goalkeepers.”
Cech has been Chelsea’s senior goalkeeper for a decade and Mourinho is not ready to end the 32-year-old’s career at the London club.
“I want to keep him and the club wants to keep him. Hopefully he stays. No player is happy when they’re not playing every game but I know Petr and he will not relax.
He will not sit in a chair and say ‘I have no chance’. He will be the opposite so I’m expecting him to go the training ground on Wednesday and to be a top professional and to fight to go back into goal,” Mourinho added.
Courtois was beaten by a superb strike from Scott Arfield as newly promoted Burnley stunned Chelsea by taking the lead.
But three goals in 17 minutes gave Chelsea the points thanks to Diego Costa’s first for the club and further goals from Andre Schurrle and Branislav Ivanovic.
Schuerrle’s goal was created by a superb pass from new signing Cesc Fabregas, with Mourinho convinced the former Barcelona and Arsenal midfielder is going to be a key player for his side as they look to challenge for the Premier League title.
“Fabregas was our first choice for that position,” said Mourinho.
“I know clearly the player because we have worked for so many years in the same league in England and in Spain.
In Barcelona he was playing so many positions but he knows better than me his best position and he is giving us exactly what we need which is that stability and that quick thinking in midfield.”
Burnley couldn’t repeat their famous win over Manchester United from the first home game of their last taste of the Premier League in 2009/10.
But manager Sean Dyche believes the experience of starting against a title contender will help them in their quest to avoid a repeat of their instant relegation last time.
“There has to be a reality to what we are hoping to achieve this season and I think that is the top of the market, or up there. It’s fair to say they have so much quality in all areas they can hurt you.
It’s a big learning curve for us but I think we started at the top end and we will learn from that experience. We kept a competitive edge and that’s important,” he said.