The Foxes were excellent, with Riyad Mahrez and Jamie Vardy to the fore, at Stamford Bridge and might have emerged with all three points had Ben Chilwell's second-half sending off not changed the complexion of the game.
Chilwell's 68th-minute dismissal for two yellow cards allowed Chelsea to push forwards and Kasper Schmeichel saved Marcos Alonso's stoppage-time free-kick.
It was Chelsea's third successive goalless draw in all competition - for the first time in their history - following stalemates with Norwich and Arsenal.
"We played with tiredness today," Conte said. "We suffered a lot first half, at the start of the second half. When I decided to put fresh energy (substitutes Willian and Pedro), the game changed. We created chances to score.
"We didn't suffer defensively. Then we tried to win the game. At the end the result was fair."
Meanwhile, the Italian insisted Chelsea's goalscoring issues are not the responsibility of one man, after striker Alvaro Morata's scoreless run extended to five games.
Conte added: "The problem is for the team, not only for Morata. Compared to last season we are conceding less, we are showing great solidity defensively. At the same time we're showing not great quality in our finishing.
"We have to improve if we want to score and we want to win. If you don't score, you're lucky the game finishes 0-0."