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 was a painful moment for Atletico and, after finishing as Champions League runners-up in 2014 and 2016, they are now consigned to the Europa League.
"It's part of football. It hurts but there are no excuses. The responsibility is ours," Simeone said.
"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.
"We tried to play our game. We created many chances to score. When you play this way and create so much you must be satisfied," Conte said.
"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.
With Roma always expected to beat Qarabag, Chelsea knew only a win would be enough to guarantee top spot.
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.