City face FA Cup winners Chelsea on Sunday, their first competitive match since winning the Premier League back in May.
While Mancini admits that he wouldn't mind if they lost in the Community Shield as long as they won the title again, he also believes that it is important to get the season off to a winning start.
"If at the end of this season we win the Premiership, it's better that we lose against Chelsea, but I think it's important we try to win," said Mancini.
"We haven't won this cup for a long time and I think it'd be important to start the season with a victory.
"But we know it will not be easy because Chelsea are a strong team, they won the Champions League and have bought four or five new players."
City get their title defence underway against newly-promoted Southampton on August 19.