City surrendered their 5-3 first-leg advantage as they lost 3-1 at Stade Louis II, exiting the competition at the last-16 stage on away goals.
Manager Pep Guardiola's bold attempts to combat Monaco's dangerous forwards by going with an all-out attacking approach himself backfired as City failed to gain any meaningful first-half possession.
By the interval they were 2-0 down after goals from Kylian Mbappe and Fabinho, and although Leroy Sane put City back in control, a powerful header by Tiemoue Bakayoko settled the tie.
The loss realistically leaves the FA Cup as City's only remaining route to silverware this season, but a quick response is required ahead of a vital Premier League clash against top-four rivals Liverpool on Sunday.
Right-back Sagna said: "It is a massive disappointment. We forgot to play in the first half, we forgot to fight as a team, defend as a team and press as a team. We gave them too much respect and against these kind of players, we put ourselves in danger.
"We have to congratulate them, they are through. We are out and we have to recover because on Sunday we have an important game.
"I expect a reaction from the team. I expect more desire, to show more passion. We did show passion in the second half but it is not enough.
"We have to recover because it was quite a difficult game and then we have to think about Liverpool."