Chelsea's unbeaten start to the Premier League season ended with a 3-1 defeat at Wembley, in which they were 3-0 down after only 54 minutes.
Sarri was far from pleased with his side's display and this week criticised Kante specifically for failing to stick to his position to the right of Jorginho in the three-man midfield.
The decision to single out one of Chelsea's star performers over the past two seasons was a surprise, but Willian insists all the squad need to sharpen up.
"Always in football you have to improve, even when you are winning games," he said. "I think every player has to improve. Even when you play good, you have to continue, you must not stop. Not only N'Golo, but every single player has to improve."
Willian has started 11 league games under Sarri, having only been in the first XI 20 times in a difficult season under Antonio Conte in 2017-18.
The Brazil international is now determined to move on from those troubled months, saying: "I don't want to go to talk about Antonio Conte. He already stays in the past.
"This season is very different from last season. We enjoy, we play football. We have a manager that wants to play football and we are happy for that."
Willian is likely to start Sunday's game against Fulham, although Callum Hudson-Odoi will hope to be involved after a sparkling display against PAOK on Thursday.
Although the 18-year-old threatens his own spot in the team, Willian is happy to advise his rookie team-mate to help him develop.
"Of course, I give him advice. I think we have to do it," he said. "The players that are here a long time do this a lot for the younger players. I've already told him that I will be his agent in the future!
"Sometimes, it's difficult [to break into the first team]. You want to show everything in one game. You want to take the ball, want to dribble, want to shoot, want to run, want to do everything as much as possible to show your quality, to show everything.
"Sometimes, you make mistakes in that but you have time to learn. He is only 18 and I think he has a lot of time to learn.
"He has the potential. He has talent, he has everything to become in the future one of the best players. Now it's early to say that. But maybe in five years we can see."