Mbappe missed a penalty as Athletic won 2-1 at San Mames on Wednesday night.
Afterwards, Mbappe posted to social media: "Bad result. A big mistake in a game where every detail counts. I take full responsibility. It's a difficult moment, but it's the best time to change this situation and show who I am."
Fede Valverde also did not duck responsibility, admitting his mistake in the play that led to Athletic's winner: "It was a hard blow, but I take the blame, I face it and I apologise.
"For my teammates and the fans. I know that it's football and these things can happen, but they are not beyond me and I did not want to stop expressing myself for the mistake I made.
"There is still a long way to go, many competitions and I am sure there will be many joys."