The Premier League champions suffered a 3-0 defeat to Arsenal in the Community Shield on Sunday after they endured relentless pressure from a vibrant Gunners side during the first half at Wembley.
David Silva's halftime introduction gave City fresh impetus as Stevan Jovetic headed against the post, but Olivier Giroud's dipping strike from 25 yards settled matters.
Pellegrini admitted his team was off the pace, insisting it must improve a great deal on that performance if they are to beat their rivals to the title once again.
"During the first 45 minutes, Arsenal scored two goals. We improved in the second half, we had chances to score, but they had a chance and scored from it," he told BT Sport.
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"I think, in the Premier League, you have five or six teams who can win the league because all have a strong squad. We must demonstrate from the beginning why we won the title last year."
Without captain Vincent Kompany, Pablo Zabaleta, Martin Demichelis and new signing Bacary Sagna because of the quartet's late return from World Cup commitments, City's makeshift defense endured a torrid afternoon.
It is an area of his squad that Pellegrini hopes to strengthen over the coming days with the signing of center back Eliaquim Mangala from Porto - a transfer saga that has dragged on throughout the offseason - and he is confident of getting the deal over the line.
"Some papers are maybe missing, but we continue having interest in the player," the Chilean said. "He wants to come so we will see what happens in the week."
In Kompany's absence, Yaya Toure took the armband for City - returning to competitive action following an offseason during which his future in Manchester was thrown into doubt by bizarre revelations from the player and his agent expressing unhappiness with how the club marked his 31st birthday.
Toure - who also suffered the tragic loss of his younger Ibrahim to cancer in June - was a goalscorer when City lifted the Community Shield with a 3-2 win over Chelsea in 2012, and he pointed to its subsequently lackluster title defense as a reason not to read too much into Sunday's result.
"It's quite difficult because we don't have all the lads back from the World Cup, but it's [good for] the fitness for the beginning of the season," he told City's official website. "We need to work hard and bounce back against Newcastle because it's going to be a very, very important game."