The Hatters bowed out of the competition at the fifth-round stage following a heavy loss to Pep Guardiola's men, who were led by two eye-catching performances.
Erling Haaland managed to breach the net of Luton goalkeeper Tim Krul five times at Kenilworth Road before being replaced by Julian Alvarez on the 77th minute.
Playmaker Kevin De Bruyne also racked up the goal contributions in Bedfordshire, providing four assists for his Norwegian teammate against the Hatters.
Apart from the disappointment of exiting the FA Cup, Luton also suffered an injury problem when defender Bell was substituted in the first half.
With the Citizens racing into a two-goal advantage early on, Bell went down following a challenge and was ultimately unable to continue playing.
Despite first-team defender Gabriel Osho sitting on the bench, the Jamaica international was replaced by 18-year-old Joe Johnson, who made just his fifth senior appearance for Luton.
Speaking after the full-time whistle on Tuesday night at Kenilworth Road, Hatters boss Edwards provided a slight insight into Bell's injury and reasoning behind the first-period substitution.
"Not too much at the moment (update on Bell's injury), he wasn't fully fit going into the game but Gabe (Osho) wasn't either," Edwards told Luton Today after the Man City defeat.
"And then when I was going to bring Gabe on, Gabe was saying he was feeling it in the warm up as well, so Gabe did not come on, so it was young JJ (Johnson), all the best mate, get on there against this lot!"
Luton will be able to call on the services of Manchester City loanee Issa Kabore on Saturday evening against Aston Villa, though, with the youngster unable to feature on Tuesday against his parent club.
Bell joins a number of first-team defenders in the medical room at the moment, including fellow centre-backs Mads Andersen and Tom Lockyer, who will not play again this season following a cardiac arrest in December.
The Hatters are also without key players in more-advanced positions on the pitch, such as nine-goal striker Elijah Adebayo, who is not expected back until the middle of March due to a thigh strain.
Aiming to close the four-point gap to 17th-placed Nottingham Forest and safety, Edwards's side will welcome Unai Emery's men to Kenilworth Road on the weekend.