Blaise Matuidi says there is more to come from France despite Didier Deschamps' side booking a place in the World Cup knockout stage with a game to spare.
Olivier Giroud's shot deflected over goalkeeper Pedro Gallese off defender Christian Ramos, giving 19-year-old Mbappe a tap-in from a few yards out to ensure the South Americans - without a goal or a point - cannot qualify.
Regardless of their flat performances in Russia, France are in the last 16, but Matuidi said Les Bleus - last champions in 1998 - can improve.
"It is a great satisfaction to have two successes in two matches," Matuidi - who started against Peru after being benched against Australia - told beIN SPORTS.
"In the game, we can do better. We did what it took to win, we had chances in the first period. We responded to Peru at the physical level, too.
"The opponent did what was necessary to put us in difficulty. They were pushed by a super support, we felt like playing away.
"In our weak times, we have been solid anyway. It's difficult for everyone in this World Cup. Congratulations to Peru who are eliminated despite a good match."
27 - N'Golo Kanté already made 27 recoveries this World Cup tournament (incl. 13 v Peru), only one French outfield player managed to reach that tally in 2010 or 2014 (Paul Pogba, 28 in 2014). Giant. pic.twitter.com/FyYosVf3NK— OptaJohan (@OptaJohan) June 21, 2018
Hugo Lloris became the first France goalkeeper to reach 100 appearances for his country and the captain said Deschamps' men will not slack off in their Group C closer.
"The substitutes have brought a lot, with their energy, to allow us to keep the result. We could have risked a little more with the ball."