Last year Ferran Soriano said he wanted five major trophies - “the Champions League, the Premier League or the FA Cup” – in five years.
Pellegrini won the Premier League and the Capital One Cup in his first season after taking over from Roberto Mancini.
But he insists that he is focusing on winning every tournament the club is involved in, and is not driven by Soriano’s target.
"I don't have a target to win five titles. Every time I play a competition, I want to win it. But that thing that we have to win five titles in five years - for me it is not important," he said.
"For this year, our target is exactly the same as last year. We will play in the four competitions we must play in and we will try to continue in all competitions as far as we can. Exactly the same as last year.
"We continue trying to win the Premier League, the FA Cup, the Capital One Cup and the Champions League, and we will see during the season what we can do."
City have so far made five new signings this summer in goalkeeper Willy Caballero, defender Bacary Sagna and midfielders Fernando, Bruno Zuculini – a deal completed late on Friday - and Frank Lampard, who has joined from the club's American sister outfit New York City FC on loan until January after leaving Chelsea.
Pellegrini feels he has a stronger squad than last season, but is not making any wild predictions about what they might achieve in the next ten months.
Asked if the group he has are capable of winning the Champions League in 2014/15, he said: "I don't know. It is impossible for me to know the future.
"The only target of our squad is the same as last year - to try to win the four competitions that we are going to play."
The first chance of silverware comes on Sunday when they face Arsenal in the Community Shield at Wembley – and Pellegrini is not expecting the match to be a typical pre-season affair.
"Of course it is not a friendly match," the 60-year-old said.
"It is an important game against an important team in Arsenal. Maybe both teams do not arrive in our best moment because both have a lot of players who are just getting back after the World Cup.
"But I think it will be a very good game, it is important for both teams to try to win it, and we will try to do that."