City have spoken in bold terms of their ambition to win five competitions in the next five years and Pellegrini appears in no doubt such expectations can be met.
Pellegrini intends not only to not improve on City's poor record in the Champions League but also to win more domestic silverware.
The Chilean begins his career in English football as Newcastle visit the Etihad Stadium in the first Monday night fixture of the new Premier League season.
Pellegrini said: "For me the Champions League is very, very important but so is the Premier League.
"I will try to play for the four - FA Cup, Capital One Cup, Champions League and Premier League - to try to win them all.
"We have a strong squad to try to win it all."
City have spent almost £90million improving their squad over the summer, bringing in midfielder Fernandinho, winger Jesus Navas and strikers Stevan Jovetic and Alvaro Negredo.
Forward Carlos Tevez is the only regular frontline player to have left following last year's runner-up finishes in the Premier League and FA Cup.
With the central midfield area now looking particularly well stocked, there has been speculation over Gareth Barry's future, with the England international entering the final year of his contract.
Pellegrini wants to keep the 32-year-old in his squad, and believes Barry also wants to stay, but does not know what would happen if an offer came in.
Asked if Barry was part of his plans, Pellegrini said: "It depends on what he wants.
"In the position of Gareth we have also (Jack) Rodwell, (Javi) Garcia, Fernandinho and Yaya Toure.
"I spoke with Gareth. He wants to stay here and he does not have any problems staying here to fight for his position like any other player in the squad.
"If he wants to go because has better options - it depends on what he wants to do.
"But he is here and in the squad. He is one player more and we will try to use it (squad) the whole year, depending on the performance of all them."
City's decision to sack Mancini at the end of last season was controversial, coming just a year after the Italian guided them to the Premier League title.
Pellegrini's track record in terms of major honours hardly compares to that of Mancini, and the former Villarreal, Real Madrid and Malaga coach has much to live up to as he enters English football.
He also has none of the Premier League experience that respective new Manchester United and Chelsea managers David Moyes and Jose Mourinho possess.
Yet Pellegrini, whose calm confidence has won many fans over already, is confident of hitting the ground running.
He said: "I don't think it can be a problem for me.
"I have a lot of experience in different countries and know a lot of things about the Premier League, so I don't think I give any hand to other managers.
"I am always watching different matches, so of all the Premier League teams I have the information I need here."
The 59-year-old also brushed away suggestions he might be nervous ahead of the first match.
"No, absolutely not," he said calmly. "I have a very good squad so I am not nervous.
"There is excitement - just like the first time in football, that is why I am still here.
"But nothing is different, just like every year I start seasons in different countries."
Such are the hefty demands placed on Pellegrini by City, he is not only expected to win silverware but to do so in style and with a harmonious dressing room.
There are also other responsibilities relating to the club's "holistic approach" to footballing matters but Pellegrini is taking the issue in his stride.
He said: "For me, my target is City must improve in all aspects. Last season it was a pity that Man City didn't win at least the FA Cup. I think we must improve in Europe also.
"We have a strong team and the target of the club is to play Champions League, not only the group stage but to continue in the competition.
"We also have to work very hard to win and bring the Premier League here.
"The style of football is a different style. Maybe we will need some time to try to play the way I want, but the targets for me and the club are always the highest."