Fabian Delph's messy clearance from Nabil Fekir's simple cross from the left.
Mikel Arteta said Manchester City have the "best players in the world" and is delighted to still be at the club after a potential move to Arsenal did not materialise in the summer.
City's troubles deepened when Fernandinho was caught in possession again.
Aymeric Laporte nearly broke the deadlock for Pep Guardiola's charges in the 17th minute with a header at the back post, but unfortunately his effort came off the crossbar.
Fekir then made it 2-0 in the 43rd minute after being set up by Memphis Depay.
"I don't think [it was a problem], we worked the last two days, focusing with him", he said. The difference is we will have some rules, you must respect.
Arteta claimed his side's reaction in the second half was superb, not an adjective that many Mancunians present would have selected, although he was probably correct in saying City created more chances after the interval than before it, even if that was not saying a lot.
Bernardo Silva pulled a goal back midway though the second half after Leroy Sane's introduction breathed fresh life into City but Pep Guardiola's men went down to their fourth consecutive Champions League defeat - making them the first English side to endure such a run.
Meanwhile, defending champions Real Madrid take on Roma, who have previous when it comes to upsetting Spanish opposition in Europe following their stunning comeback against Barcelona last season.
"It's a very open Champions League, that was the case last season and will be this season".
"But that means we're doing things really well".
City are among the favourites to lift the trophy in Madrid in June but despite believing City have the strongest squad, Arteta said it was hard to look beyond Real after winning it in each of the last three seasons - even without Cristinao Ronaldo and Zinedine Zidane.