Roberto Mancini has raised his first concerns about the new spending restrictions placed on him by Manchester City, after revealing that he could have only one striker and two fully fit central midfielders available for the FA Cup third-round tie against Manchester United on Sunday.

Mancini's plans have been disrupted after Ivory Coast reneged on an agreement and informed City that they want Yaya and Kolo Touré to report for the Africa Cup of Nations on Saturday.

Mario Balotelli has been ruled out with an ankle injury and with Gareth Barry suspended and Edin Dzeko receiving treatment for a knee problem, the richest club on the planet are in the incongruous position of struggling to fill their substitutes' bench for a Cup tie that will bring together the Premier League's first- and second-placed teams.

Mancini wants to bring in at least one new signing this month – and ideally three – but the Italian manager has discovered over the past few weeks that City are unwilling to provide the necessary money, because their last financial figures revealed an annual loss of nearly £200m. At first, Mancini was led to believe the club could buy as long as they sold first but that position has altered and the Italian is starting to fear that he may be denied funding even if the club manage to sell the Argentina striker Carlos Tevez for more than £20m.

"For Sunday, we have 17 players and I don't think we will fill the bench," he said. "In January – and I said this two months ago – we could have a big problem. We play four important league games, big games, without Yaya. If we have strikers injured then we need to buy another and at the moment I have only one striker [Sergio Agüero]. So I have one striker and only two [central] midfielders [James Milner and Nigel de Jong]. We are losing two players for a month and if we lose another we are going to need more players."

Mancini clearly intended to send a message to City's acting chief executive, John MacBeath, at a time when his team have moved three points clear of United at the top of the league. Mancini wants to sign Daniele De Rossi from Roma, knowing that the Italy international may be available for as little as £5m because he will be out of contract in the summer. However, De Rossi's salary requirements have been described as "Tevez-level" and Uefa's incoming financial fair play regulations have put immense pressure on City to reduce their costs.

Mancini, who also said that the midfielder Samir Nasri is doubtful for the United match, because of the illness that ruled him out of Tuesday's win over Liverpool, was asked if it had been made clear to him that he had no money to spend.

"Yes, yes, this is the problem," he said. "But if we don't have the players, it's tough for us. We are not United. United and Chelsea have won trophies for many years. This could be our first championship for many years and we need to do everything we can to win it. We could take in one player. We have been at the top since the start of the season and deserve it, until now. But the season is long and it will be hard.

"We have a problem because Yaya is an important player for us. Kolo is different because we have eight defenders and if we are lucky and don't have injuries I don't think we will have a big problem. But in midfield we have a big problem and, for Sunday, we have only two players there."

This indicates that Mancini still does not have enough faith in the fitness of Owen Hargreaves to use him as anything more than a substitute and it is beginning to look as if the former United midfielder will not be offered a new deal at the end of the season.

Mancini's complaints about depleted resources are unlikely to find any sympathy at United, where Sir Alex Ferguson was missing 15 players through injury or illness at one stage in the Christmas period. Mancini, however, believes that the long list of absentees at Old Trafford reinforces his case that City need more players, arguing that his team would not be able to cope if they were to experience similar problems.