Real lost 4-2 in extra-time on Thursday night.
Nacho said: "It hurts to go out because at this club the demand is paramount and we always want to be in contention for every title. Logically, it was not the objective to lose here today.
"We wanted to continue in a competition that we are very excited about. It's not going to tarnish anything, we're very confident.
"We lost today, but overall we played a very comprehensive game. We have to learn from our mistakes."