Already trailing 3-0 from last week's first leg at the Bernabeu, two early Cristiano Ronaldo penalties at the Vicente Calderon on Tuesday night sealed Los Rojiblancos' fate.
Simeone said on www.clubatleticodemadrid.com: "After losing the tie and being knocked out, we are not happy about how it happened and it is logical and normal not to be happy.
"Last year we reached the final and won the cup, and this year we reached the semi-finals. You can always do better but I think it is not bad, being as competitive as we have been in the Copa del Rey.
"The team did not lose face."
The Argentinian acknowledged his game-plan to try to overcome the first-leg deficit had not worked.
"I always think that when you're losing 3-0 is difficult trying to climb fast," he said.
"We wanted to get the ball, but could not. We tried recovering the ball in the middle with Koke, (Jose) Sosa, Mario (Suarez), Diego and (Cristian) Rodriguez to attack on the wing with (Javi) Manquillo and (Emiliano) Insua.
"This did not work out. The responsibility is mine, but the words do not count if they are not during the game."