Germany and France met in Munich on Thursday and, although neither side could come up trumps in the 0-0 Nations League draw, Mbappe made an impression despite the world champions looking a little rusty.
The 19-year-old troubled Germany's defence with his trickery, clever movement and general game intelligence.
But for Muller, Mbappe was at his most potent when he stepped on the gas.
"He has an engine in his butt that everyone else wants to have," the German forward joked.
"He makes one fast step and leaves the opponent behind. You have to defend players like him with more than one player, even if he leaves one player behind the next one has to try to stop him.
"That's the only way you can stop remarkable players like him. Of course, he had some moments during the game that the spectators enjoyed."
Thursday's contest was Germany's first since World Cup humiliation, as they were dumped out in the group stage after a 2-0 defeat to South Korea in Kazan.
Since then, the furore surrounding Mesut Ozil's international retirement and his allegations of racism against the German Football Federation (DFB), which have been denied by the governing body, has dominated talk around the national team, and Muller concedes they went into the match under significant scrutiny.
"We had a lot of pressure before the game," Muller said. "But we responded in the way we had to.
"You have to make distinctions. It wasn't our best game and we have a lot to pay back. That was the first key step, but that's all."