Alvaro Morata was ruled out of the Premier League clash on Saturday after picking up his fifth booking of the season as he celebrated his match-winning goal in the Blues' EFL Cup quarter-final win over Bournemouth.
The Spaniard's absence meant that Antonio Conte opted to start Eden Hazard up front but, despite the Belgian looking sharp, neither he nor substitute Michy Batshuayi could find a way past a tenacious Toffees backline.
"Coming here was always going to be tough, they're on a good run so we expected a tough game but we tried our best to win," Courtois told Sky Sports News after the game.
"Their goalkeeper made a few good saves and we had to be careful on the counter but other than a few free-kicks they didn't have many chances.
"It's not easy when a team falls back, I think we could've had more shots on target but we didn't have a big guy up front despite lots of crosses into the box.
"We concentrated hard on keeping the clean sheet, which is a good thing from today of course, but we're not happy we didn't create the chances to score."
Chelsea remain third in the Premier League table, two points behind Manchester United.