Theo Walcott capped a spell of Arsenal pressure to scramble home an equaliser five minutes before the break - but they were on terms for only two minutes before Sergio Aguero's powerful finish put City back in front.
The Gunners had actually dropped 4 from their previous 5 Premier League games, as well as dealt with City in unpredictability surrounding manager Arsene Wenger's future, with even more demonstrations presented prior to kick-off.
"I would like to thank the fans", Wenger told Arsenal Player. You could say mathematically it's not good for them or for us.
Arsenal remain seven points adrift of City in fourth, albeit having played a game fewer, while Pep Guardiola's team sit 11 points behind league leaders Chelsea.
The Arsenal boss was speaking as a small band of supporters gathered outside the club's training ground to continue the growing protests against Wenger. If we show the same spirit we showed against City [in Sunday's 2-2 draw], we will win football games.
The Gunners last finished outside the top four in 1995-96, when they had to settle for fifth place the season before Wenger's arrival.
Derrick Rose to have knee surgery again, miss rest of season
Thus ends a star-crossed season that began with a rape trial and pretty much sucked in a way that only a Knicks season can suck. Rose tore his ACL in the 2012 playoffs, then missed the full 2012-13 season.
About 1,000 Arsenal fans joined an anti-Wenger march before the game, the biggest such protests against the Frenchman. We want to be further up the league and we have dropped two more points. I don't understand. Our job is to perform as long as we are somewhere.
Like Wenger, Danny Welbeck praised his team mates' character in fighting back, but conceded that there was room for improvement as Arsenal look to salvage a testing campaign.
Former Manchester United and England global Gary Neville has slammed the German's lack of commitment in the incident, insisting that he should have shown more fight, especially with Wenger's job said to be on the line. The worst time in a football game to concede is just before half-time.
Arsenal had to do without Laurent Koscielny in the second half after the defender suffered an injury to his Achilles and was replaced by Gabriel.
Guardiola said: "Yesterday was the first day he started to go to the pitch to run and walk. That is why he helped us a lot in the second half to do that".