One of City's signings was Blackburn's loss in the form of Roque Santa Cruz with the striker, who is not fit to play on Saturday, the most high-profile of several players to leave Ewood Park during a frugal summer.
Maintaining a squad fit to compete has been no easy task, and Allardyce will count a season of stability as a success after the club flirted with relegation before finishing 15th last campaign.
"A lot of players left here as well as Roque Santa Cruz this year," Allardyce said.
"Matt Derbyshire, Tugay, Andre Ooijer, Aaron Mokoena, Carlos Villanueva, then Danny Simpson going back.
"We've lost a huge amount of players and not too many people have printed that, but it's a big ask to replace all those and get better.
"We hope we have but we won't really know until the season gets under way."
Having brought in Croatian international striker Nikola Kalinic and opened talks to sign up former Real Madrid right-back Michel Salgado, Allardyce feels he has enough at his disposal to stay well away from the relegation zone.
He continued: "The ambition is for each player to improve in his game by one per cent. I think if every individual does that then we will be in mid-table or the top half, so I'm not asking a great deal.
"If everyone does that and you times it by 38 games then you are really going to get where you want to go.
"We've set realistic targets and we've spoken to the players about those targets, we've focused their goals on what they want to achieve, and we want to do it as a team.
"If we get all that right, and the attitude and team spirit, we'll be fit enough to compete with anybody in this league. That in itself will bring us more wins than defeats this season."
Allardyce warned his opposite number Mark Hughes of the problems that could lie ahead if his team of new signings fails to gel immediately, although the Blackburn boss conceded City now had match-winners in their ranks that would always give them a chance.
"The quality of player they have got means that, even if they are not playing as a team, an individual can produce at any given time that outstanding talent that they have paid for," Allardyce said.
"Irrespective of how they are playing and how well you are defending, it can be impossible to stop that talent producing a match-winning opportunity for Manchester City.
"That's what they've got now, and not just one or two, but three, four or five.
"We're going to have to be right on top of our game, make sure we suppress that side of Manchester City and try and expose the weaker sides that they have."
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