An early Koke goal at the Vicente Calderon gave Diego Simeone's side a 2-1 aggregate win over the Catalans, who have failed to reach the semifinals of the competition for the first time since 2004-05.
Though Neymar is keen to move on from the defeat quickly, he was full of admiration for how the Rojiblancos played throughout the last-eight tie.
"The truth is that we started the match badly," he told reporters. "In the first 20 minutes, we conceded and that made the match difficult. We can only congratulate them. They started the two games better. Both in the first leg and the return game, it was difficult to break them down and they just have to be congratulated.
"We have the Copa del Rey and La Liga left and we have to try. You have to keep your head up. Life goes on. We feel sad, losing is not easy."