Spanish champions Atleti were ruthless in a 4-0 victory at the Vicente Calderon, as two goals in either half kept Diego Simeone's men in the race for the Liga title.
Goalkeeper Casillas believes there is little point in dwelling on the defeat because the team were so badly outplayed and is keen to quickly avenge the defeat in Real's coming matches.
"Analysing the game is a mistake. Atletico were better than us, they beat us all over the park," Casillas told reporters.
"They were superior and we have to congratulate them because they played a perfect game. We were lacking in every aspect of play.
"We leave here with heavy hearts, but we have to correct the mistakes so they don't repeat themselves again in the future.
"We also have to ask the fans for forgiveness because we are the last people who want to give this image of ourselves.
"It was a tough defeat. We have to get on with it, keep face and focus on the next match. We weren't at our best. We are responsible for conceding four goals.
"I'm not going to make excuses for myself because that would look like I was trying to distance myself from any of my mistakes."
