The Chilean took over at the Etihad Stadium in July after Roberto Mancini was sacked for finishing last season without winning a trophy.
Pellegrini will take charge of his first league game at home to Newcastle on Monday and he admits the settling in period will be short.
"We have to hit the ground running and that starts against Newcastle," he told the club's programme.
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"We now start a new cycle after Roberto Mancini’s work from the previous seasons. He created history here, brought the club its first silverware in a long time and the first title in 44 years. He will never be forgotten and shouldn’t be.
"But football moves on and evolves, it has always been that way, and now we have a new era starting tonight with some new players. We had a good squad before I got here but I think we have bought well and bought wisely during the summer.
"Supporters of Manchester City have the reputation of being a big family and I am delighted to be part of it. My job now is to win trophies and take the team forward."
Pellegrini has bolstered an already impressive squad with the signings of Fernandinho, Jesus Navas, Alvaro Negredo and Stevan Jovetic at a combined cost of more than £90 million.
And the 59-year-old feels the most important thing is to have cover for every position if City are to challenge for titles this season.
He added: "The aim has been to build a group that has two top-class players for each position; we are fighting for trophies on four fronts so we will need everyone at some stage.
"The Premier League can be won by one point and that point can depend on having a squad with strength and depth.
"Part of my job is to manage the fitness and freshness of the players to give us the best possible chance of winning all those trophies for which we compete."