3-0 at Juventus on Tuesday night as Fabio Quagliarella, Arturo Vidal and Sebastian Giovinco scored.
Chelsea (2-2-1) dropped into third place in Group E and can advance only if it beats Nordsjaelland (0-4-1) on Dec. 5 and Shaktar Donetsk (3-1-1) wins at home against Juventus (2-0-3).
"It's a big disappointment," Chelsea manager Roberto Di Matteo said. "It's been a difficult evening for us, for the team, for the club. So there was a lot of reflection. "It's mathematically still possible, and you always try while there's still hope. Who says Juve are not going to lose against Shakhtar? We have to do our own job against Nordsjaelland."
Chelsea also is winless in four straight Premier League games.
"I'm responsible for the resul., I'm responsible for the performance, and tonight was negative," Di Matteo said. "If anyone has to take the blame, it's me. I select the team. The blame belongs to me."
Shakhtar beat Nordsjaelland 5-2 as Luiz Adriano scored a hat trick and Willian had two goals.
Lionel Messi had his ninth two-goal game of the season, and Barcelona won 3-0 at Spartak Moscow 3-0 to reach the knockout rounds for the ninth straight season. With 56 Champions League goals, Messi tied Ruud Van Nisterooy for second in career scoring, trailing only Raul Gonzalez (71). Messi also has 80 goals for club and country in 2012 — 68 for Barcelona and 12 for Argentina — and is five behind the single-year record set by Gerd Mueller for Bayern Munich and Germany in 1972.
"Messi is a perfect player, maybe the best player in the world right now," Spartak coach Unai Emery said.
Bayern Munich, Shakhtar Donetsk and Valencia also advanced. Already assured of a berth in the second round, Manchester United rested many regulars in a 1-0 loss at Galatasaray.
Two weeks after beating Barcelona at home, Glasgow Celtic lost 2-1 at Benfica and dropped into third in Group G behind its Portuguese opponent on head-to-head record. Ola John put the hosts ahead in the seventh minute, Giorgos Samaras tied it in the 32nd and Ezequiel Garay scored on a volley in the 71st.
Barcelona (4-1) leads Group C, followed by Benfica and Celtic (both 2-2-1) and Spartak (1-4).
Celtic hosts Spartak on Dec. 5, while Benfica travels to Barcelona.
Bayern and Valencia (both 3-1-1) each advanced from Group F with a 1-1 tie in Spain that eliminated BATE Borisov (2-3). Valencia, playing a man short after Antonio Barragan's 33rd-minute ejection, went ahead on Sofiane Feghouli's goal in the 77th. Thomas Mueller tied it five minutes later with a shot that grazed Feghouli.
Lille (1-4) win 2-0 at BATE on goals by Djibril Sidibe in the 14th minute and Gianni Bruno in the 31st.
United (4-1) didn't use Wayne Rooney, Robin Van Persie, Ryan Giggs or Rio Ferdinand in its loss at Galatasaray (2-2-1), which got a 53rd minute-goal from Burak Yilmaz — who has all five of his team's Champions League goals this season. Galatasaray is second in Group H on head-to-head over Cluj, which beat visiting Braga 3-1 behind Rui Pedro's hat trick. Cluj visits United in its last group game while Galatasaray travels to Braga.