Another sanction means City can only spend £49m on players this summer, as well as any transfer fees they receive.
And their wage bill for 2014-15 must stay the same as this season.
Paris St-Germain, one of eight other teams to breach the rules, have been handed a similar fine and cap as City.
A City statement said that they only fielded 21 players in the Champions League this season, were not planning to spend a net amount of more than £49m on players this summer and expected their wage bill to be lower next season anyway.
"At the heart of discussions is a fundamental disagreement between the club's and Uefa's respective interpretations of the FFP regulations on players purchased before 2010," it read.
"The club believes it has complied with the FFP regulations on this and all other matters.
"In normal circumstances, the club would wish to pursue its case and present its position through every avenue of recourse. However, our decision to do so must be balanced against the practical realities for our fans, for our partners and in the interests of the commercial operations of the club."
It added: "The nature of conditions that will result in the lifting of sanctions means that the club expects to be operating without sanction or restriction at the commencement of the 2015-16 season.
"Importantly all non-financial sanctions agreed to would have been complied with as a natural course of the Club's planned business operations."
Clubs who breached the rules had to reach a deal with Uefa, which City have done, or else take it to an adjudicatory panel in June.
The other clubs guilty of breaking the rules were Russian sides Zenit St Petersburg, Rubin Kazan and Anzhi Makhachkala, Turkish clubs Galatasaray, Bursaspor and Trabzonspor and Bulgarian club Levski Sofia.
City posted combined losses of almost £149m for the past two seasons - £97m in 2012 and £51.6m in 2013.
Uefa introduced FFP because it fears many clubs are risking their futures by spending beyond their means, while Uefa president Michel Platini also believes the big spending of some clubs is ruining the game.
PSG's failure to adhere to FFP is understood to stem from the club's controversial contract with the Qatar Tourism Authority.
The contract is said to have been ruled as valid by Uefa but the overall value of the deal - worth up to £165m per year - has been deemed excessive.
PSG are also understood to have argued with Uefa that French income tax levels in France made complying with FFP that much tougher.
Sources close to the club say that, over a three-year period, they will pay £163.9m more in wages than an equivalent club based in Germany because of taxation.
Uefa ultimately rejected the club's argument that they have to pay higher gross salaries to attract and keep their star players.
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