Roma, who defeated Qarabag 1-0 at home, leaped to top spot and secured qualification for the round of 16, leaving Atletico in third place.
The draw for the Champions League last-16 will take place next weekWhen is the Champions League draw? Atletico, losing finalists to Real Madrid in 2014 and 2016, were ultimately made to pay for two draws against Champions League debutants Qarabag, after both Roma and Chelsea saw off the Azeris twice. Jose Mourinho's men look capable of a decent run in Europe too this season, although they will want to avoid Real Madrid and Bayern in Monday's draw for the knockout stage.
A host of other sides are also still in with a chance of progressing.
Last season's runners-up Juventus would have expected to have qualified before the final matchday when they were drawn in Group D alongside Barcelona, Sporting Lisbon and Olympiakos, but they head to Athens on Tuesday still needing a win to definitely progress.
That turned out to be enough for Roma to win the section ahead of Chelsea, who had to come from behind to draw 1-1 at home to Atletico.
Stefan Savic put into his own net from an Eden Hazard cross to level the scores and send them into the Europa League.
Group C: Atletico Madrid needs a lot to happen to keep alive its streak of four consecutive appearances in the knockout stage.
The asterisks denote teams who are not yet assured of their current qualifying positions.
Unai Emery's side beat Bayern 3-0 in Paris and have a better goal difference, so the German champions must win by four goals if they are to finish top.
In Munich, Robert Lewandowski and a double from Corentin Tolisso, sandwiching Kylian Mbappe's reply, gave Bayern a confidence-boosting win over PSG.
"I am 50 percent happy and 50 percent disappointed", said their coach Unai Emery.
Basel won 2-0 at Benfica to qualify second. Despite a fifth loss in six group games, they limp into the Europa League in the new year.
Depending on how results fall tomorrow night, Shakhtar Donetsk could be replaced by Serie A giants, which would be a much more menacing proposition for United, while Porto could be replaced by Red Bull Leipzig and a Spartak Moscow victory over Liverpool at Anfield would fire the Russian club into the final 16.