The PSG star missed the vital spot-kick as Les Bleus were eliminated by Switzerland in the last 16 of the tournament and French Football Federation (FFF) president Noel Le Graet says he considered walking away from the national team following the criticism aimed in his direction.
Le Graet told French media: "I met with him after the Euros, he felt that the Federation had not defended him after his missed penalty and the criticism on the networks.
"We met for five minutes in my office. He was angry, he didn't want to play for the French team any more - which he obviously didn't mean.
"You know how it is, he's a winner, he was very frustrated, like all of us, by the elimination.
"He's so media-friendly. He's a great guy, much more collective than people think."
Mbappe had suggested last year that he would no longer play for his country if he was considered to be a "problem" for the team.
He said: "I have never taken a single euro to play for the French national team and I will always play for my national team for free. Above all, I never wanted to be a problem.
"But from the moment where I felt like that I was starting to become a problem and that people felt I was a problem… I received the message, that my ego was what made us lose, that I wanted to take up too much space, and that without me, therefore, we might have won.
"The most important thing is the French national team and if the French national team is happier without me, [I'll go]."