Mbappe scored twice in a 2-1 victory over Denmark as the 23-year-old became the second player after Brazil great Pele to score seven or more World Cup goals before their 25th birthday.
“What can I say about Kylian?,” said France manager Deschamps, who is seeking to repeat Les Bleus’ 2018 World Cup triumph in Qatar.
“I’ve said it time and time again. He is decisive and makes a difference. He is an exceptional player in an exceptional team.
“There are two types of leadership – physical and mental – and Kylian is a leader.
“Kylian doesn’t speak, he’s not very talkative, but he’s like a steam train on the pitch and gets the crowd going.
“He knows from the get-go that the French team needs him and he needs to be at his best.”
Mbappe scored in France’s opening 4-1 win over Australia and now has three goals in the race for the 2022 World Cup’s Golden Boot award.
France still have top place to secure in Group D when they play Tunisia on Wednesday, but Deschamps suggested that he will make changes for that game.
He said: “We now have peace of mind going into the third game because we are in the round of 16.
“Hopefully we are going to finish top of the table and I’m not going to take any risks.
“That is the advantage when you win your first two games, you can take your foot off the gas.
“Let’s not getting carried away, but the players work well as a team and we have a great spirit on and off the pitch.
“The Danish put up a good fight, but in the second half we created a lot more chances.
“There are a couple of things we could clean up – how we put in that extra effort and find the space in attack – but it was a good performance.”
Denmark had equalised through Andreas Christensen’s close-range header, seven minutes after Mbappe had broken the deadlock with a smart finish just after the hour mark.
But Mbappe had the final word four minutes from time, finding space at the far post to divert home Antoine Griezmann’s cross off his thigh and reward France’s superiority with three points.
Denmark head coach Kasper Hjulmand said: “We can’t argue too much (with the result), but we were close to getting the draw.
“Football is such small margins. We didn’t create more chances in Paris when we beat them (in the Nations League), but it goes the other way.”
The Euro 2020 semi-finalists, having drawn their opening game with Tunisia, must beat Australia on Wednesday to reach the round of 16.
“It’s make or break,” said Hjulmand, who hopes to have injured captain Simon Kjaer available on Wednesday.
“We are very disappointed, but we’ll pick it up and get back on track for the game. We will be ready.
“We had zero points after the first two games of Euros and we still have hope.”