The Premier League champions endured relentless pressure from a vibrant Arsenal side during the first half at Wembley and Arsene Wenger's men were duly rewarded by goals from Santi Cazorla and Aaron Ramsey.
David Silva's half-time introduction gave City fresh impetus as Stevan Jovetic headed against the post before Olivier Giroud's dipping strike from 25 yards settled matters
Pellegrini told BT Sport: "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.
"These things happen before the season starts.
"It was not the pace we played in pre-season but I will talk with the players and I am sure we will be ready to start the Premier League.
"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 due to the quartet's late return from World Cup commitments, City's make-shift defence endured a torrid afternoon.
It is an area of his squad that Pellegrini hopes to strengthen over the coming days with the signing of centre-back Eliaquim Mangala from Porto - a transfer saga that has dragged on throughout the close-season, with complications surrounding the player's current third-party ownership status understood to be the sticking point.
Nevertheless, the City boss is hopeful the France international Mangala can be in place by the time his players begin their quest for a third Premier League title in four seasons at Newcastle United next weekend.
He said: "Some papers are maybe missing but we continue having interest in the player, he wants to come so we will see what happens in the week."
