Juventus eliminated the reigning champions by beating Shakhtar Donetsk 1-0 on Wednesday, with Galatasaray and Celtic also qualifying for the last 16 in a thrilling final round of group-stage matches.
Chelsea needed to better Juventus' result in Ukraine to finish second in Group E, and kept its part of the bargain by thrashing FC Nordsjaelland 6-1 for Rafa Benitez's first win as interim manager.
It was in vain, however, as Olexander Kucher's own goal earned Juve victory and top spot ahead of Shakhtar.
"We knew it could happen, unfortunately the damage had been done before," said Chelsea goalkeeper Petr Cech, whose side became the first reigning champion to exit at the group stage.
Galatasaray beat Braga 2-1 to finish ahead of CFR Cluj, which won 1-0 at below-strength Manchester United, in Group H. Celtic defeated Spartak Moscow 2-1 in Group G thanks to a controversial late penalty to oust Benfica, whose 0-0 draw at Barcelona was marred by a left knee injury to Lionel Messi.
Lying on a stretcher, Messi was driven off the field on a cart, jeopardizing the Argentina star's hopes of breaking Gerd Mueller's 40-year-old scoring record for a calendar year. Messi has 84 goals, one less than the German great, with four more games left in 2012.
"Tests have confirmed tonight that the player Leo Messi suffered a bone bruise on the outside of the left knee," Barcelona said in a statement, adding that he could be fit for the La Liga match against Real Betis on Sunday.
Messi had gone on as a second-half substitute, with Barca already qualified for the knockout stage.
Bayern Munich topped Group F by thrashing BATE Borisov 4-1, finishing ahead of Valencia despite the Spanish side's 1-0 win at Lille.
Both Bayern and Valencia were already sure of going through.
Chelsea, Cluj and Benfica will bemoan the fact that they have been eliminated despite picking up 10 points from six matches, a tally that would usually put a team through.
It was a bittersweet night for Benitez, who claimed a first win in four matches since being parachuted in as a replacement for the fired Roberto Di Matteo. He will also have welcomed the sight of Fernando Torres returning to form, scoring two goals to go along with strikes by David Luiz, Gary Cahill, Juan Mata and Oscar.
Luiz's was a penalty, one of three conceded in seven second-half minutes — two to Chelsea and one to the Danish visitors. Two were missed.
In the end, however, Chelsea's blitz of goals were for nothing, leaving the team to fight it out in the Europa League with the eight other third-place finishers in the Champions League. Chelsea finished level on points with Shakhtar, but fell down on the head-to-head record.
"The game was out of our hands," Benitez said. "I said before that we had to do our job and, as a manager, you have to be really pleased with the performance of the team."
With Manchester City also out, it also means only two English teams qualified for the last 16 for the second season running.
Juventus leapt above already-qualified Shakhtar thanks to Kucher's own goal, the defender diverting Stephan Lichtsteiner's low cross into his own net in the 56th minute.
"Our goal was achieved — we advanced to the next stage," Juventus coach Antonio Conte said.
Like Chelsea, Cluj couldn't have done any more, beating United thanks to Luis Alberto's superb swerving effort in the 56th minute at Old Trafford.
At that stage, Galatasaray was 1-0 down at Braga but goals by Burak Yilmaz and Aydin Yilmaz turned the game on its head and helped the team through to the knockout stage for the first time in 11 years.
United was already guaranteed first place and played largely a reserve team.
Benfica, which wasted some great chances in the Camp Nou, was also close to going through only for Celtic to be awarded a debatable penalty in the 81st minute against Spartak. Kris Commons stepped up and smashed the kick in off the crossbar.
"The players have been magnificent — it is a monumental achievement on their behalf," said Celtic manager Neil Lennon, whose team beat Barcelona at home earlier in the group stage.