The Chilean is hoping for a win against Arsenal at Wembley on Sunday as his side prepare to defend their Premier League crown over the next nine months
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Only one win came from City's opening six away league fixtures as they were beaten by Cardiff City, Aston Villa, Chelsea and Sunderland.
Pellegrini is keen to avoid a repeat of that run of results this time around, and is targeting a win in the Community Shield against Arsenal.
"We want to start the season much better than we did last year," Pellegrini told a media conference.
"We started poorly away from home and it took us time to repair the damage done by dropping so many points early on.
"Winning the FA Community Shield would be the ideal start to the campaign.
"We had two very good games against them [Arsenal] last season, winning one and drawing the other and, each time, they were very difficult but very different games.
"Arsenal have brought in some new players, as have we, and just like last season, I expect both teams to be among five or six sides challenging for the Premier League title."
The Chilean's side will have an unfamiliar look to it at Wembley as a host of City's star players - including Vincent Kompany, Sergio Aguero and Pablo Zabaleta - only returned to training this week following their World Cup exploits.