Ferran Torres struck midway through the first-half as Barca won the second-leg 1-0 at the Metropolitano to reach the final 5-4 on aggregate.
However afterwards, Simeone said: "We didn't have a good first half, nor do we have to apologize. In football, sometimes you go through situations where the opponent is superior, but in the second half, we competed very well and were able to get a draw.
"I didn't expect to play the whole game like we did in the second half. We were playing against a great opponent, and we have to accept the position we're in.
"The team is competing very well. We're going to continue competing in the same way, with the same work we're doing, and focus on La Liga. Starting Friday, we'll focus on Sevilla."
Simeone insists Atletico have shown they're on the level of Barca and Real Madrid this season.
"I have no doubt that the club is pure growth, we have brought in great players who are performing at a high level, we are competing well in the Champions League, in the League and in the Cup, I will not move away from what I have said.
"They could have scored a few more goals and given us the chance to bravely face the second half. We tried, but the opponent plays very well. I like the way Barcelona plays, and we competed very well in the four games we played against them."