Portuguese star is sorry for the humiliating defeat at the hands of Mourinho's side, but vows to bounce back in this week's Copa del Rey tie against Los Blancos
The one-sided contest saw Madrid score five times in the first half, and the 31-year-old Portuguese international was involved throughout.
“They are a strong team, but we cannot be so vulnerable. It cannot happen again, for us to concede so many goals in such a short time,” Costa told reporters.
“In the first few minutes we were at the same level as Madrid, but they scored with their first counter-attack, we tried to balance that out, and then they scored the second."
The opportunity for revenge is on the horizon, however, as the two sides again face each other at Mestalla in their Copa del Rey quarter-final second leg clash on Wednesday.
Costa is well aware that an improved performance is imperative as they look to overturn a 2-0 deficit from the first leg.
He added: “We have to win on Wednesday. We know that Madrid will be more relaxed and it will be a totally different game.
“We must play with our head, unlike on Sunday, where we were open all over the place, because we cannot have the same story again.”