Real's French attacking star missed from eleven meters against Liverpool in the Champions League last week.
Still, Mbappé got the trust again when Real Madrid got a penalty at a 0-1 disadvantage in Bilbao. But Julen Agirrezabala could save the fairly weak penalty.
"A big mistake in a match where every detail counts. I take full responsibility for it", Mbappé writes himself on Instagram after the match.
"A tough moment, but it's the best time to change this situation and show who I am".
A little later, the equalizing goal came after all when Jude Bellingham, in the 78th minute, scored a rebound after a shot from Mbappé.
The joy in the Real camp was short-lived. Federico Valverde fumbled with the ball and Athletic's substitute Gorka Guruzeta scored the winning goal 2-1 in the 80th minute.
Real Madrid is second in La Liga football and is four points behind Barcelona, which they have a game in hand on. Athletic is fourth and has eight points up to Barça.