Chelsea were held to their third consecutive goalless draw in all competitions by Leicester, who were reduced to 10-men after 68 minutes.
It means Chelsea are 15 points behind leaders Manchester City and coming under threat from the chasing pack in the race for the top four.
The home fans at Stamford Bridge were far from happy with the efforts of their players with Tiemoue Bakayoko among those being criticised.
But after the match, Courtois blasted the Chelsea fans, claiming their complaints are not helpful to the team.
Courtois said: ”It doesn’t help when the fans boo and whistle after each misplaced pass.
“We didn’t play well but that’s when we need the fans behind us.”
Alvaro Morata was another player who struggled, failing to score for the eighth time in the last 10 games.
But Chelsea boss Antonio Conte defended his striker saying the team is not creating enough chances.
He said: “I don’t think it is only Morata’s problem, also the other players, because we are not scoring goals, we are not conceding, but we are not creating chances.”