The new City manager faced the press for the first time since his appointment and outlined his ambition to deliver success with style at the Etihad.
And the immediate priority is to fill the hole in his squad left by Carlos Tevez's departure for Juventus.
Pellegrini said: "I spoke with Carlos a couple of weeks ago and I feel he didn't want to stay here anymore. He was very clear to tell me. It was the best choice for him and the club.
"We have two strikers at the moment and we need another one. I won't name names at the moment. We need two players in every position and we will try to do our best to get them."
The Chilean claimed his attacking philosophy was among the qualities which earned him the chance to succeed Roberto Mancini.
A repeat of 2011's Premier League triumph is also on the agenda along with an upturn in Champions League form following successive failures to escape the group stage under Mancini.
He said: "One of the important reasons I'm here is the way my teams have always played. We are going to play an attractive game, always in the opposite side, always an attacking team.
"Five or six teams are always trying to win the Premier League and I'll try to do that with Manchester City.
"I think that the Premier League is so important, as is the Champions League. I know the last two years weren't good for Manchester City in Europe, but I'll try to change that."
Pellegrini will now take a strong squad to South Africa, where City face Supersport United on Sunday and Amazulu the following Thursday.
Marquee summer signing Fernandinho will be among the squad on the flight out, and the Brazilian is looking forward to life at City.
He told the assembled media: "Manchester City is considered one of the best clubs in the world. I have come to win as many medals and trophies as possible. That is my main aim.
"I want to play well and if I give good performances then I think the fans will like me."
No matter where City finish in the table, the season's two Manchester derbies provide another unofficial prize for the rival managers and fans, with the Citizens celebrating three victories from the last four league derbies.
Pellegrini added: "I know the most important thing for City fans is to beat United. I'm sure we will do it and this year, the same as other years, we will be on top of United.
"I also played United twice with Villarreal in the Champions League, in 2006 and 2009, and both times we qualified for the last 16 and they didn't."
The club's hierarchy have spoken of a desire to win five trophies in the next five seasons and Pellegrini has also been told to improve City's brand of football.
When asked about the trophy target, the 59-year-old jokingly said: "Just five?" before giving a more considered response.
He said: "We will try to work and do our best here and then we will see how many trophies."