Atletico required maximum points from their final Group C fixture to stand any chance of progressing, but the three-time European runners-up could only draw 1-1 at Chelsea.
Saul Niguez had Atletico on track for victory at Stamford Bridge before Stefan Savic turned the ball into his own net as the Spanish side finished third, four points behind group winners Roma and Chelsea.
Atletico head coach Simeone, however, was relatively upbeat post-match as he looked ahead to the Europa League – a competition won twice by the club.
"We didn't fail. This sort of thing can happen. They gave it their all to win and try to go through until the last minute. We're fine," Simeone said.
"What's important is to be decisive. You need to score. We only lost one game [in the UEFA Champions League], in the 93rd minute. No excuses – we'll be rated at the end of the season.
"It's now a new challenge for us. New dreams to fight for."