Defending champions France beat Poland 3-1 to book a quarter-final spot, but they did not have everything their own way at Al Thumama Stadium on Sunday.
Poland created a number of first-half chances before Olivier Giroud settled French nerves with a goal just before half-time.
Mbappe then stole the show in the second half, thriving on the extra space Poland afforded him scoring two excellent goal before Robert Lewandowski scored a late consolation.
And Deschamps admitted to the French press after the game that his team will keep looking to Mbappe to produce such moments of individual quality in subsequent knockout games.
Mbappe is now leading the race for the Golden Boot with five goals at the tournament.
“It was not easy because this Polish team was well organised to upset us,” Deschamps said.
“But we always have this ability to find a lot of togetherness. And after that, it’s Kylian, with the ability he has to solve many problems, which is so much to our benefit.”
On the spirit within the French camp as they look to become just the third team in history to defend the World Cup, Deschamps said: “There has been unity since the start.
“Obviously, being a quarter-finalist is something very good, it just makes all that happen. It is shared joy.”
France face England in the quarter-finals on Saturday.