The result means the Blues missed the chance to leapfrog Manchester United into second place in the table, and it was also the club's third goalless draw in a row in all competitions.
However, Courtois said the team need the fans' support, per Gary Taphouse at Sky Sports:
Chelsea were far from their best against Leicester City and were fortunate not to be behind at half-time as the Foxes had the better chances.
Shinji Okazaki fired a good opportunity over the bar, and Courtois had to make a diving save from a Wilfried Ndidi header.
The Telegraph's Matt Law said he had not seen a worse performance from Chelsea this season:
Manager Antonio Conte opted to make changes in the second half and took off talisman Eden Hazard and Cesc Fabregas.
The decision to take off the Belgian was booed by some supporters, per Law:
Leicester were reduced to 10 men on 68 minutes when Ben Chilwell was sent off after picking up his second booking of the afternoon for a foul on Victor Moses.
However, Chelsea could not take advantage of their extra man as Leicester comfortably held on for a deserved point.
Goal's Nizaar Kinsella noted how fans also booed at full-time:
It was another disappointing result for Chelsea and followed on from Wednesday's goalless draw against Arsenal in the first leg of their Carabao Cup semi-final and last weekend's 0-0 draw with Norwich in the FA Cup third round.
Kinsella noted how long the Blues have now gone without a goal:
It's also the first time in their history that Chelsea have drawn three consecutive games 0-0, per Opta:
Chelsea's problems stem from their key attackers being out of form. Striker Alvaro Morata has now gone five games without a goal, while Eden Hazard has just one goal and one assist in his last 10 outings.
Substitutes Pedro and Willian could not impact the game after they were introduced, and Conte looks to have a big task on his hands to get his team back in form and firing again.