The Frenchman has called for calm from his team-mates and urged his side to "keep pushing" as they lost more ground in their battle for Champions League football next season
The Gunners were comfortably beaten by the Premier League champions after Laurent Koscielny was sent off in the opening 10 minutes, and though City captain Vincent Kompany was later sent off, Arsene Wenger's side could not recover the two-goal deficit.
However, Sagna says his team-mates need to stay strong, and wants the players to show mental strength in fighting for a Champions League spot.
"We can't let our heads go down. First of all we need to rest because we play in two days [against Swansea]," he told the club's official website.
"After that we just need to keep pushing because we have many games to come back and we are not far from third position, so we have to keep the heads up.
"To play 11 v 11 against City is very hard, even if you are at home, but 10 against 11 is even harder.
"It is harder to play on the pitch and it is hard to have control of the ball, so we have to look forward to the next game and keep our heads up.
"City have some quality players, we have some nice players as well, but with one more on the pitch than us it makes it very difficult.
"Of course we had to keep going and try and score the first goal [of the second half], and we could have come back because it has happened in the past but it didn't happen.
"We knew it would be a tough game with hard tackles and desire, and of course they wanted to win as much as we did."