Atletico Madrid will be missing from the Champions League knockout phase for the first time in five years. Requiring a win at Chelsea to have any chance of advancing, Atletico was held to 1-1 in its final game in Group C at Stamford Bridge on Tuesday.
"We're sad," Atletico goalkeeper Jan Oblak said. "We have to pick our heads up."
Even if Diego Simeone's team had held onto the lead secured by Saul Niguez, it would not have been sufficient to finish in the top two since Roma beat Qarabag 1-0 to join Chelsea in the next round as group winners.
Madrid, twice a finalist in the last four years and a semifinalist last season, will instead be back in the Europa League for the first time since the 2012-13 season.
"I wouldn't say it's a failure because we knew it could happen," Simeone said through a translator. "Everything that is bad we turn into a positive."
It didn't go Chelsea's way either at home, toppled from top spot after failing to win the meeting of the third-place teams in England and Spain.
The Premier League champion's defense crumbled the 56th minute, when former Chelsea striker Fernando Torres flicked on a corner that the unmarked Saul Niguez nodded past goalkeeper Thibaut Courtois.
"We have to improve because after a corner there were a lot of mistakes," Chelsea manager Antonio Conte said.
It took an own-goal to equalize in the 75th minute, with defender Stefan Savic diverting Eden Hazard's shot into his own net.
With Chelsea finishing second to Roma, the Italian capital club could have the more favourable fixture in the round of 16 in February. The draw is on Monday in Nyon, Switzerland.
Atletico lost only once in the group stage, and only when it conceded in the fourth minute of stoppage time at home to Chelsea. Another costly result was a home draw with Azerbaijani newcomer Qarabag in October.
"It hurts (being eliminated) because it's part of football," Simeone said. "We have no excuses. The responsibility is ours. The game against Qarabag at home, we had 10 chances to score and we were not able to win."