The reigning Premier League champions were unable to find a breakthrough against Claude Puel's stubborn visitors and failed to make numerical advantage count when Foxes full-back Ben Chilwell was sent off 20 minutes from time.
The result represented the third goalless stalemate in the space of a week for the Blues, who were held both by Arsenal in the semi-finals of the EFL Cup in midweek and by Championship side Norwich City in the FA Cup last weekend.
"Obviously we wanted to win the game, and at the end with 10-men we pressed them, but for 70 minutes of the game they were the better team," Courtois told Match of the Day.
"Obviously we all feel a little bit tired, last year we went from week to week, but now we have already played a lot of games. But it's not excuse, Leicester had more intensity than us and more aggression, they started very offensive and pressed us high up the pitch.
"Having the replay against Norwich didn't do us a favour, because we have lost the recovery week, but now we have another important game, because we want to go far in the FA Cup like last year. We just have to keep working and keep trying to win every game."
Antonio Conte's side welcome the Canaries to Stamford Bridge on Wednesday night before travelling to Brighton & Hove Albion in the league next weekend.