Playing a fifth game in 15 days, the Blues struggled to break down a lively Leicester City side who were playing with 10 men for the final 25 minutes after Ben Chilwell’s second yellow card.
It was a third 0-0 draw on the trot in all competitions, after stalemates with Norwich City in the FA Cup and with Arsenal in the EFL Cup.
“It doesn’t help when the fans boo and whistle after each misplaced pass,” Courtois told reporters after the game.
“We didn’t play well but that’s when we need the fans behind us.”
Chelsea missed the chance to, temporarily at least, move second in the Premier League as they lose further ground on both Manchester United and table-toppers Manchester City.
Next up for Antonio Conte’s side is the FA Cup reply with Norwich City at Stamford Bridge on Wednesday.