The former Malaga boss met the press for the first time since his appointment as Roberto Mancini's replacement and spoke of his desire to bring success back to the Etihad Stadium.
"We have very good players and we can reach important targets," said the Chilean.
"We will try to do the very best that we can and then we will see how many trophies we can win.
|MANCHESTER CITY LATEST
|12/5||Manchester City are 12/5 with Coral to win the Premier League
"When Manchester City won the Premier League it was one of the most important moments in the club's history and well try to repeat it.
"One of the most important things for City fans is to beat Manchester United and we will try to do that. This year, the same as in other years, we will try to be on top of United."
Pellegrini has already acquired Brazilian midfielder Fernandinho and Sevilla's Jesus Navas, but admitted he was in the market for more players, particularly in the striking department following the departure of Carlos Tevez.
"We only have two strikers at the moment and we need another one but I am not going to talk about rumours. When players arrive then we will talk," Pellegrini continued.
"We need a very good squad, a strong squad with two players for every position."
Pelligrini was also non-committal on the futures of Gareth Barry and Joleon Lescott, who both have been linked with moves away from the club this summer.
"In the next few weeks we will consider all the situations for different players," he added.
"We will sit down with Txiki Begiristain [the club's sporting director] and with the players and discuss the situation."