It was a depressing evening for both clubs at Stamford Bridge on Tuesday as neither got what they wanted from their final group fixture.
Atletico had to win to have a chance of advancing, but although Saul Niguez's second-half header put the visitors ahead, Chelsea drew level through a Stefan Savic own goal.
In the end, Roma's win against Qarabag in the other group match made the result irrelevant for Diego Simeone's team, who failed to qualify for the last 16 for only the second time and the first since the 2009-10 season.
"It's part of football. It hurts but there are no excuses. The responsibility is ours," Simeone said.
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"This can be a new challenge. Everything bad we can make into a positive."
Chelsea were already through to the knockout stages, but blew their chance to finish in first place and in theory earn an easier draw.
Having lost and drawn against Roma, Chelsea finished second behind the Italians due to their inferior head-to-head record.
That is bad news for Antonio Conte's side, who could be pitted against Champions League heavyweights including Barcelona and Paris Saint-Germain in next week's last 16 draw.
"Our opponent (in the next round) won't be happy to play against us."
Atletico striker Fernando Torres endured a difficult three-and-a-half years with Chelsea, but he came close to giving his side an early lead on his return to west London when his shot deflected onto the roof of Thibaut Courtois' net.
Unlike Torres, his compatriot Alvaro Morata has had no problems adapting to life at Chelsea and he showcased his deft touch to make space for a curling shot that flashed just wide.
Again Morata went close to the opener when he stretched to meet Victor Moses' cross, but Atletico goalkeeper Jan Oblak spread himself to block the Spaniard's close-range effort.
Causing Atletico all manner of problems, Morata almost caught out Oblak with a dipping strike from wide on the left that had the keeper scrambling to save.
- Slack marking -
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Davide Zappacosta was next to test Oblak when the Chelsea wing-back unleashed a fierce shot that was pushed around the post.
Despite that barrage, Filipe Luis, another Chelsea old boy in the Atletico side, almost put the Spaniards ahead against the run of play when his long-range shot cannoned back off a post to Koke, who should have done better than head straight at Courtois.
Sparked by that near-miss, Atletico snatched the lead in the 56th minute.
When Torres flicked on a corner, Niguez easily escaped Tiemoue Bakayoko's slack marking and had the simple task of heading home from close range.
Pedro fared no better when his back-heeled flick was saved on the line by Oblak.
Chelsea's pressure finally brought an equaliser in the 75th minute as Hazard's shot was deflected into his own net by Savic.
Morata should have put Chelsea ahead moments later, but he shot too close to Oblak.
There was more angst to come for Chelsea in the closing minutes when Willian missed a sitter before Michy Batshuayi's stinging strike whistled wide.
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