The reigning Barclays Premier League champions had not won at the home of the Gunners since 1975, but eased to victory thanks to goals from James Milner and Edin Dzeko.
Arsenal's task of beating the champions, who remain seven points adrift of leaders Manchester United, was made harder when defender Laurent Koscielny was sent off after just 10 minutes.
France international Sagna admits it was always going to be difficult once referee Mike Dean had brandished an early red card, even though Dzeko missed the resulting penalty.
"To play 11 v 11 against City is very hard, even if you are at home, but 10 against 11 is even harder," Sagna told Arsenal Player.
"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.
"It is always nice to see a goalkeeper saving a penalty but it is difficult to play.
"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."
Milner scored a great first goal and Dzeko atoned for his penalty miss by tapping in a second before half-time, although City's day was ruined slightly by captain Vincent Kompany's late red card.
However, Sagna was pleased with Arsenal's general response in the second half.
"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," he said.
"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."
Arsenal do not have long to wait until they can put things right on the pitch, as they welcome Swansea to the Emirates Stadium for an FA Cup third-round replay on Wednesday evening.
The Swans caused an upset when they recorded a 2-0 win at Arsenal on December 1 and Michael Laudrup's side remain in good form, having won the opening leg of their Capital One Cup semi-final at Chelsea last week.
Sagna wants the players to be confident ahead of their replay, which will see the winners face Brighton in the fourth round, and then keep the momentum going in the fight for a third-place finish in the league.
"We can't let our heads go down," he said. "First of all we need to rest because we play in two days.
"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."
The defeat leaves Arsenal sixth in the table, three points behind Everton with north London rivals Tottenham a further three clear in fourth.
The Gunners do have a game in hand over their nearest opponents, however, after their Boxing Day clash with West Ham was rearranged for January 23 following a strike from London Underground workers.
Gunners' boss Arsene Wenger had urged his players to be aware of their own ability and start games quicker.
"The team is desperate to do well and has quality," he said.
"We need to be conscious that we have quality and we have to show more authority from the start in big games. The authority comes with the confidence in your quality."
Wenger confirmed after the match that midfielder Mikel Arteta will be missing for around three weeks with a calf injury.
The Frenchman recalled Abou Diaby, who had not featured since September due to a thigh problem, to replace Arteta and felt his compatriot did a good job for the team.
"Diaby became stronger during the game," Wenger said.
"I feel he was like the team. He started very slowly and became stronger in the second part of the game.
"I took the gamble (of starting Diaby after his injury lay-off) because I feel that it was needed. It's good that he came through well. He will become stronger very quickly."
Premier League Top 4 Finish 12/13 Top 4 Finish: Arsenal 4/11
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