The Barclays Premier League champions are without a host of players for the third-round tie against the npower Championship side at the Etihad Stadium.
Last season's top scorer Sergio Aguero is out with a hamstring injury while midfield driving force Yaya Toure is now heading for the African Nations Cup with brother Kolo and back-up striker Abdul Razak.
Forward Samir Nasri is suspended while defenders Aleksandar Kolarov, Maicon and Micah Richards, and midfielder Jack Rodwell, are on the injury list.
There has been speculation over whether Mancini might allow some players to leave this month to allow for potential new arrivals but he insists he cannot let anyone go yet.
He said: "To leave - not one player (can) because, for example, tomorrow [Saturday] we have 16 (players).
"We have to put two young players on the bench. We need time to decide this. We have one month to decide this.
"The FA Cup is totally different from the Premier League. Probably for Watford it is the most important game in the year and we won't change a lot of players - we don't have the players."
The tie brings Mancini up against his fellow Italian and former rival Zola.
The pair, both renowned forwards, were regular opponents in Serie A and competitors for a spot in the national side.
Zola enjoyed the more internationally celebrated playing career but Mancini has had the greater success in management in stints at first Inter Milan and now City.
Zola is now trying to establish himself with the Hornets after his previous two-year spell in charge at West Ham ended with his sacking in 2010.
Mancini said: "I respected him as a player when he played and now as a manager. I think he did a good job when he was at West Ham and now with Watford.
"He was a fantastic player, his quality was of top level.
"He did very well in Italy, and very well in England with Chelsea.
"As a manager you need time but he still did very well with West Ham and I think he has a good chance to bring Watford into the first division because he knows football very well."
In the build-up to the game, Zola has recalled an "unbelievable" goal Mancini, playing for Sampdoria, scored against his Napoli side in the 1990-91 season.
Contributing to what proved a telling victory in the title race, Mancini struck with a volley from the edge of the box and Zola still rates it as "one of the best" he has ever seen.
Mancini, however, has played that down, saying: "I don't remember, it was a long time ago."
The build-up to the game for City has been overshadowed by the latest controversy surrounding enigmatic striker Mario Balotelli.
Mancini and Balotelli have been pictured grappling in a training-ground bust-up but the incident has been played down and the forward could be on the bench after overcoming a virus.
City are hoping Aguero's injury is not serious and he could be back in action next week.
Mancini said: "Sergio is out for tomorrow [Saturday]. We hope he can recover for Arsenal."