Chelsea made just one change from Wednesday’s Carabao Cup semi-final first leg against Arsenal with Gary Cahill coming in for Andreas Christensen.
Cahill was then forced off after 30 minutes with a hamstring problem and Christensen came on in his place.
And the Blues struggled throughout to break down their opponents even though they were reduced to 10 men when Ben Chilwell was shown a second yellow card in the 68th minute.
After the match, Conte said his players were tired following their efforts in midweek against Arsenal.
Conte told Match of the Day: “I think we played with a lot of top players against Arsenal, and then again today against a very good team.
“I think a lot of our players were tired.
“In the first half Leicester ran more than us, they played better than us.
“But we knew we were playing against a good opponent, maybe the worst opponent we could have played in this moment. We suffered a lot in the first half.”