It was a depressing evening for both clubs at Stamford Bridge on Tuesday as neither got what they wanted from their final group fixture.
Celtic claimed a Europa League berth by finishing third but did so in a disappointing fashion as they lost 1-0 at home to Anderlecht.
Elsewhere, Roma recorded a 1-0 win over Qarabag at the Stadio Olimpico. The only goal in that game was scored by Diego Perotti in the 53rd minute.
Chelsea will join them in the last 16, but ended up second in their group behind Roma. The results meant that the Italian side rose to the top of the group and Antonio Conte's side had to settle for second spot.
Napoli will also fancy their chances of making it to the latter stages of the competition after missing out on a place in the Champions League Round of 16 to Shakthar Donetsk.
Ohio State stuns MI with second-half rally
Ohio State: The Buckeyes came on strong and played stout defense to roar back and flatten their rival. The Buckeyes started the Big Ten season with back-to-back victories.
In Group D, Barcelona - who had already guaranteed to top their group - defeated Sporting Lisbon 2-0.
And when asked whether Atletico's early Champions League exit following a 1-1 draw with Chelsea would further grease the wheels for an imminent exit, Simeone was quick to play down any talk of a move away for the 26-year-old.
Sporting will continue with the Europa League while Olympiakos are eliminated. Liverpool, Sevilla and Spartak Moscow could all still top Group E.
Group H runners-up Real Madrid notched 17 as Cristiano Ronaldo made history by becoming the first player to score in all six first-phase games, while Harry Kane hit six for the section's winners Tottenham.
Which team have been the most impressive in the Champions League this season?