The defeat means Arsenal have now lost 11 games in the Premier League this season and they are 11 points off West Ham, who are fourth.
The Gunners, however, can still qualify for the Champions League if they win the Europa League and they face Benfica on Thursday in the second leg of their last-32 tie.
Arsenal drew the first leg in Rome 1-1 and as a result they lead the tie by virtue of away goals ahead of Thursday’s game in Athens.
“We have a final on Thursday because we want to continue in the competition [Europa League],” said Arteta.
“We have to sleep, eat and we won’t have time to train then we fly to Greece.
“Today they (Man City) played a little bit differently but within that organisation they can do lots of really good things. They manage the situation really well.
“When we conceded the first goal it put us in a difficult situation. It was tough. With the formation and the players they use they are really comfortable.
“After that the team reacted really well, were on top of the game and created chances but we lacked the quality in those situations to score the goal.
“We got something wrong. We didn’t do it in the first 10 minutes. It’s a cross and Raheem Sterling cannot head a ball there. You cannot concede that goal. It was a tactical thing that we were prepared for but we didn’t read it in the game.
“We got momentum and confidence and were really good on the ball as well. We found good spaces but when we were in the final third we didn't pick the right pass to score a goal.
“We tried to use some weaknesses that we thought we could exploit. They don’t have many! How they compete when they have in the last few minutes, they are a top side.”