Roberto Mancini goes into the Community Shield on Sunday believing Manchester United are "five yards" ahead of Manchester City and warning that the Eastlands club can forget about winning the Premier League unless they sign at least two more players.

City have already made the biggest signing of the summer, Sergio Agüero joining from Atlético Madrid for £38m, as well as bringing in two defenders, Gaël Clichy and Stefan Savic, but Mancini still believes the FA Cup winners come up short compared to Sir Alex Ferguson's side.

"They are on the top," Mancini said. "They're a strong team, they won the last Premier League, they have bought good players and at the moment they are over us. We are very close but United have maybe five yards more than us.

"We want to improve on last season and we'll try to win the Premier League but we need two or three more players and, if we can do that, I think we will be very close. But look at United – they have 29 senior players whereas we have 20. To be competitive, we need more. We're missing players, we don't have enough for the whole season and it's a problem. We haven't managed to get all the players we want and it is important we get them now in the next seven days."

Mancini's top target is Samir Nasri, and City's information is that Arsenal's position may be softening and that the London club may, after all, consider selling the Frenchman to another English club. Mancini, however, upset Arsène Wenger earlier in the summer by discussing his pursuit of the player so he was careful not to inflame the situation again. "It's better we don't talk about this," he said.

Costel Pantilimon, a 6ft 8in Romania goalkeeper, became City's fourth signing of the summer on Friday, joining the club for around £1.6m from Timisoara, subject to a work permit, to become Joe Hart's understudy. Alessio Cerci, the Fiorentina winger, is another target and Mancini also wants a central midfielder. "We had five last year but Patrick Vieira has retired now."

City actually have a senior squad of 24 players, even excluding Emmanuel Adebayor, Wayne Bridge, Craig Bellamy, Roque Santa Cruz and Nedum Onuoha, all of whom are training away from the main group because they do not fit into the manager's plans. Mancini made it clear he would not change his mind – "They are good players but not part of our plans," he said – even though he believes City, with their current squad size, may find it difficult to adapt to the rigours of competing for the title as well as playing in Europe.

"We need a good list of players because when you are playing in the Champions League for the first time it is very hard, totally different from the Europa League, and you need to change five, six, even seven players after every Champions League game. Tottenham struggled with this last season and we don't want to have the same problem. It's different for Manchester United, they needed only three [new] players. For them, it is easier."

City also have to clear up Carlos Tevez's position, and Mancini said he could not be certain whether the Argentina striker would remain at the club. Internazionale may be keen on a player-plus-cash exchange involving Samuel Eto'o or Wesley Sneijder. Otherwise, Mancini believes Tevez will return to training on Monday after being given a three-week break to recuperate from the Copa América.

"He's still a City player at the moment. He's a professional and, if he doesn't get another team, he'll play for us and he'll play seriously like last year." The manager spoke to Tevez for the first time in the entire summer on Monday – "His telephone is working again" – and reported that the club captain was "happy" and "told me he would come back".

Mancini believes his side will have to score "10 to 15 more goals than last season" if they want to win the league, an indication that he will be more attack-minded in the new campaign. Agüero, who, was also involved in the Copa América, will be given his debut as a substitute at Wembley, and Ferguson believes Mancini's men could provide the most credible challenge to United in the title race.

"We accept that challenge and it's good for us, as it keeps complacency away from the door," the United manager said.