The Blues played 120 minutes in the UEFA Super Cup final loss to Liverpool in Istanbul on Wednesday before facing the Foxes at Stamford Bridge four days later.
"It's true we used a long of energy this week," Kante said.
"We had the match against Man U and then travelled to Turkey for the match against Liverpool when we played very well.
"We were a bit tired against a good Leicester team. We had a good first 20 minutes. After Leicester were very good in the match and in the end a draw is not a bad result."