City beat Dynamo Kiev 1-0 in their second leg thanks to Aleksandar Kolarov's 39th-minute free kick at Eastlands but went down 2-1 on aggregate.
Liverpool couldn't break down Braga at Anfield and was held to a frustrating 0-0 draw, with the five-time European champions exiting 1-0 on aggregate.
There will be no English teams in the quarterfinals for the first time since 2008, when the competition was called the UEFA Cup.
Runaway Portuguese leader Porto advanced with a 3-1 aggregate victory over CSKA Moscow after winning the second leg 2-1 at home, while Benfica knocked out Paris Saint-Germain.
PSV Eindhoven ensured there would be no British representation in the last eight by knocking out Scottish champion Rangers thanks to a 1-0 win both in the second leg and on aggregate, while Spartak Moscow, Villarreal and FC Twente also progressed into Friday's quarterfinal draw.
Man City's cause was not helped by the sending off of Italy striker Mario Balotelli in the 36th for a studs-first tackle on Goran Popov, when the score was 0-0.
“The problem for Mario is that he thinks he could be a fantastic player. But when he does something stupid like that, it is difficult for me, difficult for him and difficult for the team,” City manager Roberto Mancini said.
Kolarov put the big-spending northwest team in front with a low drive from a free kick soon after the red card, but it could not find a second goal.
Liverpool's European campaign is also over after a lackluster display against Braga, which relied on its narrow win at home in the first leg last week.
Even with 35-million-pounds ($56 million) signing Andy Carroll starting for the first time, the Reds struggled to create many clear-cut chances.
Hulk and Colombia midfielder Fredy Guarin were the first-half scorers for 2003 champion Porto at Estadio do Dragao, with Zoran Tosic's consolation not enough for CSKA, which succeeded the Portuguese side as the competition winner.
Benfica, 2-1 ahead of PSG from the first leg, went 3-1 up on aggregate thanks to winger Nicolas Gaitan's fierce low shot into the corner in the 27th at the Parc des Princes.
PSG leveled eight minutes later when Mathieu Bodmer's sweetly struck volley from 15 meters beat goalkeeper Roberto but Mevlut Erding and Ludovic Giuly wasted decent chances for the French side to take the match into extra time.
Russian club Zenit St. Petersburg, the 2008 winner, was behind 3-0 from the first leg at Dutch champion FC Twente but scored two first-half goals through Roman Shirokov and Alexander Kerzhakov to threaten a sensational comeback.
But the home side couldn't find an aggregate equalizer and had to settle for a 2-0 win, going out 3-2 on aggregate.
Both teams wore black armbands in memory of the wife of Zenit's first-choice goalkeeper Vyacheslav Malafeyev, Marina, who died in a car crash on Thursday morning.
Spartak Moscow routed four-time European champion Ajax 3-0 at home, thanks to goals by Dmitri Kombarov, Welliton and Alex, to advance 4-0 on aggregate but there was crowd violence before the match.
The Interfax news agency reported that two Spartak fans were stabbed by a man from Russia's volatile region of Dagestan. All three were taken to the hospital, Interfax reported.
Fights also broke out among groups of Spartak fans in the Moscow subway, with Russian news agencies reporting at least 60 arrests.
PSV eked its way through thanks to Jeremain Lens' 13th-minute winner, but Rangers was denied what appeared a clear penalty when United States midfielder Maurice Edu's shot looked to be handled on the line by Atiba Hutchinson in the second half.
In the other last-16 match, Giuseppe Rossi became the competition's leading scorer with eight goals by scoring what proved to be the winner for Villarreal in a 2-1 victory over German side Bayer Leverkusen.
The Italy striker set up Santi Cazorla for the opener in the 33rd at El Madrigal before the midfielder returned the favor in the 61st, Rossi firing in right-footed for his 26th goal of the season.
Leverkusen pulled one back through Derdiyok in the 83rd but the Yellow Submarine advanced comfortably 5-3 on aggregate.
