In Pep Guardiola's 100th Champions League game as City coach, his team struggled to cope with Bayer Leverkusen's quick transitions in a 2-0 defeat on Tuesday (Wednesday AEST), while Barcelona had an own goal and a red card in their 3-0 loss at Chelsea.
Guardiola made 10 changes to his starting line-up following Saturday's Premier League loss to Newcastle, with Erling Haaland among those on the bench, but it didn't have the desired effect.
Alejandro Grimaldo fired home Leverkusen's first goal with a low shot into the far corner in the 23rd minute, and Patrik Schick headed in a second in the 54th minute.
"It feels wonderful and we gave everything till the last second," Schick told broadcaster DAZN.
City could have moved atop the table with a win, but the night ended with the top three unchanged. Bayern Munich, Arsenal and Inter Milan all play on Wednesday (Thursday AEST).
Borussia Dortmund rose to fourth and Chelsea are fifth after both won to join City on 10 points, while Barcelona are 15th and Juventus improved to 21st with a win.
Club world champions Chelsea comfortably beat 10-man Barcelona 3-0 to earn their third league-phase win and move closer to the top.
It was the second loss for Barcelona, who went down a man after defender Ronald Araujo was shown a second yellow card before halftime.
The hosts scored with an own goal by Jules Kounde in the 27th minute, a nice strike by Estevao in the 55th and a close-range shot by Liam Delap in the 73rd minute.
While Guardiola had an unexpected loss, his old foe Jose Mourinho picked up his first Champions League win with his new club Benfica as left back Samuel Dahl's early goal set the stage for a 2-0 victory over troubled Ajax as the two winless teams met in Amsterdam.
Dahl scored an unstoppable volley on the rebound after Ajax goalkeeper Vitezslav Jaros had saved a header from Benfica defender Nicolas Otamendi.
Leandro Barreiro added a second goal in the 90th minute.
Ajax have lost all five of their Champions League games and won only one of their past 10 games in all competitions.
Canadian forward Promise David scored the only goal as Belgium's Union Saint-Gilloise won 1-0 at injury-depleted Galatasaray.
The Turkish club were without injured Champions League top scorer Victor Osimhen, and finished with 10 men after 18-year-old defender Arda Unyay picked up two yellow cards.
In Naples, Scott McTominay scored the opening goal as Napoli won 2-0 against Azerbaijan's Qarabag.
Napoli fans commemorated the fifth anniversary of the death of club legend Diego Maradona.
In Prague, Athletic Bilbao were frustrated in a 0-0 draw with Slavia Prague, which leaves both clubs outside the qualifying places after five games.
In France, Pierre-Emerick Aubameyang scored twice in four minutes early in the second half to turn the game around for Marseille in a 2-1 win over Newcastle.
Serhou Guirassy scored two goals as Dortmund routed 10-man Villarreal 4-0 to end a three-game winless run in all competitions.
And Juventus won 3-2 on their trip into the Arctic Circle to face Bodo/Glimt, needing a stoppage-time winner from Jonathan David after the Norwegian hosts levelled the scores in the 87th minute.
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