The French midfielder has been ruled out of action for a number of weeks after suffering a muscular problem while on duty with his national team last week.
It is not clear exactly how long Kante will be out for but it looks as though he will definitely be sidelined for a number of weeks as he recovers from the problem.
Chelsea slumped to a disappointing defeat by Palace at Selhurst Park on Saturday as they suffered their second defeat in as many games in the top flight.
And Conte has admitted that the Blues badly missed the likes of Kante on Saturday, with striker Alvaro Morata also out injured.
Speaking at his post-match news conference at Selhurst Park, Conte said: “For us it’s a very difficult moment because we started the game without Morata and Kante, which isn’t simple.
“To lose a player like Kante is not simple because he’s able to cover a lot of the pitch, but I have to take into consideration different solutions.
“The balance is very important if we want to win. Today our balance was poor.”
However, there was some good news for Chelsea fans as Conte confirmed that he is hoping to have Morata back available for selection for Wednesday’s Champions League clash against Roma at Stamford Bridge.
The striker has been recovering at Cobham after having picked up a minor hamstring problem against Manchester City before the international break.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news