The Catalans suffered a 1-0 defeat at the Vicente Calderon on Wednesday, with Koke's fifth-minute volley ensuring a 2-1 aggregate win for Atleti, while denying Barca a seventh-straight semi-final in the competition.
The visitors had opportunities to level matters, with the likes of Lionel Messi, Neymar and Xavi all seeing chances go begging, but Iniesta conceded Atleti exerted more pressure in the opening stages and were rewarded for their efforts.
Iniesta has now set his sights on overhauling Atleti at the top of La Liga, while also pointing to Wednesday's Copa del Rey final with rivals Real Madrid as an ideal opportunity to bounce back.
"Atletico deserved to go through because they took advantage of their chances," the 29-year-old told Barcelona's official website. "Like in the first 20 minutes, they pressured us and they took advantage. We tried to score until the end of the game.
"The Champions League is a very good competition and it's a shame that we didn't make the semifinals. There aren't many league games left to win the title and we have a final in Granada this weekend and then on Wednesday in the cup."
Fullback Jordi Alba echoed Iniesta's comments, lamenting Barcelona's failure to break down a stubborn Atletico rearguard.
He added: "They were the better team in the opening minutes and after that we took control of the match, but we didn't know how to get into their area. It's very difficult to beat a rival that play in this way. After 20 minutes, the intensity was the same for both teams.
"Now we have to win the Liga and the Copa del Rey. We have to forget about this game and start over. We don't like to lose these games, especially in a competition like this one."