The French star missed a penalty as Real were beaten 2-1 by Athletic Bilbao on Wednesday (04.12.24) in La Liga and revealed his frustrations at his performances in an Instagram post.
He wrote on the social media platform: "Bad result. A big mistake in a match in which every detail counts.
"I take full responsibility. It's a difficult time, but it's the best time to change this situation and show who I am."
Mbappe has failed to set the world alight at Real since his summer move from PSG and Madrid coach Carlo Ancelotti admitted that the player "can do better".
The manager said: "He isn't at his best level, but we have to give him time to adapt.
"He's scored 10 goals, he can do better, and he's working to do better."
Mbappe's penalty miss came after he missed from 12 yards against Liverpool in the Champions League last week but Ancelotti is judging the player on more than just spot kicks.
He said: "I shouldn't evaluate a player's game based on a penalty. Sometimes you score them, sometimes you don't. Obviously he's sad and disappointed, but we have to carry on."
Ancelotti insists that Mbappe will still be considered to take penalties for Real despite his recent failures from the spot.
The Italian coach said: "He took the responsibility to take it today, and it didn't go well. But in football, that can happen."
Madrid midfielder Fede Valverde made an error in the build-up to Bilbao's winning goal and apologised for the mistake after the game.
He said: "It was a hard blow, but I take the blame, I show my face and I apologise. For my teammates and the fans.
"I know it's football and these are things that can happen, but they're not alien to me and I didn't want to stop expressing myself because of the mistake I made."