Senior stars such as two-time title winners Yaya Toure and Vincent Kompany fell below their usual high standards as City meekly surrendered the Barclays Premier League crown last season.
Consequently City were not widely tipped for the title in pre-season but Monday's impressive 3-0 opening win at West Brom has provided a reminder of their quality.
Toure and Kompany were both outstanding at The Hawthorns while another of the cornerstones of their past successes, David Silva, also shone.
Pellegrini said: "All of them, not only Vincent and Yaya and players who had a lot of criticism, they are not thinking about why they were criticised
They are thinking about their performances
They want to be important players and win titles."
City have rejuvenated their squad with the club record £49million signing of Raheem Sterling over the summer
Midfielder Fabian Delph is another fresh face while the club have also been continually linked with Wolfsburg's Kevin de Bruyne.
Yet much will still depend on the established core, which also includes the likes of goalkeeper Joe Hart and striker Sergio Aguero, and Pellegrini believes many of them are now reaching their peak.
He said: "The important thing for them is to be ambitious, to have a winning mind, to try to continue to win titles and improve in Europe
They have a lot of challenges and our most important players are in their best ages."
City face a stern early test of their title credentials as champions Chelsea visit the Etihad Stadium on Sunday.
Toure will hope to maintain the momentum after his particularly eye-catching, goalscoring display on Monday
He did leave the field with a groin problem late on but that was only a precautionary measure and he is fit to feature against Jose Mourinho's men.
The Ivory Coast international was the midfield driving force for City's last title win in 2014 but he never seemed to get going last season after much-publicised difficulties during the summer.
Pellegrini said: "Yaya is very important for us
We have important players and we can play without those players, but it is better when we have Yaya in the team and playing in a good way.
"I prefer always to play with Yaya
I hope he will be a regular for the whole year and be very important.
"He played very well (on Monday) and we all hope he will continue in the same way."
Aguero is also pushing for a starting spot
Pellegrini used him off the bench at West Brom because his pre-season was limited by international duty.
Source : PA
Source: PA