Diego Simeone's side beat Rubin Kazan 1-0 in Russia on Thursday night with a goal from Radamel Falcao but it was not enough to send them through to the last 16 after a 2-0 home defeat in the first leg.
Second-placed Atletico now turn their attentions to Sunday's home clash with Espanyol, while they also have a Copa del Rey semi-final second leg to look forward to against Sevilla on Wednesday, where they lead 2-1 from the first meeting.
Atletico maintained their perfect home record in the league with victory over Real Betis three weeks ago and will hope to preserve their four-point lead over Real Madrid.
Adrian said after their European exit: "We came close. We played the game we had to do. We were attacking, creating chances and we did not have good fortune. We tried to come through and we are pleased with our work.
"We're a little sad about not being able to continue in a competition that we have a lot of love for because we are reigning champions. It is sad not to continue but we are aware that we are doing things right.
"We have a home game against Espanyol and we want to continue the streak that we have at home in the league. Then comes the Sevilla game, which is very important. We can play in another final and we have to prepare very well."
Given their home success this season, Atletico go into the match as firm favourites, but they will face the form team in La Liga.
Javier Aguirre has completely changed the fortunes of Espanyol since taking over as manager in November.
Then bottom of the table, the Barcelona side have won five of their last six matches and are now closer to the European places than the relegation zone.