City's back line has looked vulnerable in the close season and they go into their first match at home to Newcastle United on Monday having let in eight goals in their last three warm-up matches, including a 3-1 defeat by Arsenal on Saturday.
This after boasting the meanest defence in the league last season when they let in 34 goals in 38 games in finishing runners-up to neighbours Manchester United.
In the previous season they had an even better record, conceding just 29 on their way to the title.
Having spent around 90 million pounds ($139.15 million) on forwards Alvaro Negredo and Stevan Jovetic, winger Jesus Navas and midfielder Fernandinho in the close season, it is not surprising they have also scored seven times in those games.
The trouble is that more goals conceded than netted does not add up to silverware, a challenge for a club whose chief executive has set a target of five trophies in the next five years.
There is still time before the transfer window closes at the end of the month for the wealthy club to bolster their defence but even if they do, they seem to have made it clear where their priorities lie.
Pellegrini, who replaced the sacked Roberto Mancini in June, has promised to instil an attractive brand of attacking football in his team but also knows this cannot be at the expense of City's recent strengths.
"We had problems defending and we will try to improve this week," local media quoted the Chilean as saying.
"If we buy someone, then OK. But, otherwise, we have a good squad. But, yes, we have conceded many goals, we will have to find ways to change this.
"You are always concerned when you are 3-0 down but we lost in pre-season. We did not lose three points and that is important. We will be at our best for the Premier League."
City trailed Manchester United by a hefty 11 points last season but with last term's top three sides all under new management there is a sense of unpredictability about the new season and a feeling that Pellegrini has been flying under the radar.
While new United manager David Moyes has been batting away questions over the future of striker Wayne Rooney, while also conducting a very public pursuit of Barcelona's Cesc Fabregas, second-time Chelsea boss Jose Mourinho has been chasing Rooney.
In the meantime, Pellegrini has been quietly going about his business, bringing in new players in good time while the others are most likely left to carry out their transfer activities once the season has started.
The former Malaga manager's calm manner also offers an antidote to the sometimes temperamental Mancini, whose public criticism of his players fuelled media reports of dressing room unrest last season.
City fans are still fond of Mancini after an FA Cup win in 2011 and a Premier League title the following year, after more than three decades without a trophy. But they will hope that their new manager can bring the team back together.
Goalkeeper Joe Hart, one of the shining lights in the championship-winning season, was one of those to feel the sharp tongue of Mancini last term and Pellegrini will hope he can coax him and some of the others back to their best.
Pellegrini reckons he has the right players to bring in trophies.
"I think we have the best squad in England," he told local media earlier this month.
"We bought four important players. We already had a very good team and with these four I think we improved a lot.
"We hope that from the first match against Newcastle at home we will start winning, and we will try to bring another trophy here." ($1 = 0.6460 British pounds) ($1 = 0.6468 British pounds)