Succeeding Roberto Mancini as boss over the summer, Pellegrini arrived at City with a good reputation in the Champions League, having guided Malaga to the last eight and Villarreal as far as the semi-finals.
And the Blues, now in their third successive season in the competition after debuting in 2011-12, have already experienced a landmark European moment under the Chilean this term, securing qualification for the knockout stages for the first time.
Demichelis knows Pellegrini well, having been part of his Malaga team in recent years, and from being at River Plate when he was manager there.
And speaking ahead of City's Champions League Group D match on Tuesday at another of his former clubs, Bayern Munich, the Argentina centre-back said: "I think Manuel has shown with Malaga and Villarreal what he can achieve in the Champions League.
"I think now we're on a really good path.
"We're growing with every game and every week and we have a great future ahead of us with Manuel."
Demichelis was at Bayern from 2003 to 2010, moving from there to Malaga and then on to Atletico Madrid for a brief spell before joining City towards the end of the last transfer window.
He was ruled out of playing in the Blues' home clash with Bayern in early October due to a knee injury, but is in contention to feature on Tuesday.
And the 32-year-old admits returning to the Allianz Arena is emotional for him.
"It (Tuesday's match) will be a very important occasion for me," Demichelis said.
"I played here for seven and a half years and it was great playing here for Bayern.
"I experienced a lot here, and tomorrow and even today are two very emotional days for me in my career and in my life."
Both leaders Bayern and second-placed City are already through to the round of 16 ahead of this contest, the two sides' final Group D match.
City, three points behind their hosts, can leapfrog the defending champions and secure top spot with a win - but they will have to better the 3-1 scoreline Bayern won the reverse fixture at the Etihad Stadium by to do so, which looks a tall order to say the least.
On the challenge ahead, Demichelis said: "It's very difficult to say what Bayern's weak points are but we have to play tomorrow with real fire in our stomachs.
"We're playing a great team and it's great preparation for us."
Asked if City wanted revenge for what happened in the initial meeting - where they were completely outplayed by Bayern for much of the contest - Demichelis added: "Yes.
"A lot can happen in football. Its 11 vs 11 tomorrow.
"It's very difficult to win here but we have to try to do that."