City chief executive Ferran Soriano revealed in May last year that he wanted the club to win an average of a major trophy - meaning the UEFA Champions League, the Premier League or the FA Cup - every year over the next five seasons.
Pellegrini - appointed as successor to Roberto Mancini in the same month - made a strong start towards achieving that goal by securing the Premier League title and the League Cup in his maiden season at the Etihad Stadium.
City are likely to face a stern challenge if they are to enjoy further success in the upcoming campaign, with Arsenal, Chelsea and Manchester United all having strengthened their squads in the recent weeks.
Another trophy could come City's way when they take on Arsenal in the Community Shield at Wembley.
But, speaking ahead of Sunday's clash with Arsene Wenger's FA Cup winners, Pellegrini stressed that he is not concerned with any sort of trophy target.
When asked about Soriano's comments Pellegrini said: "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.
"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 [League Cup] and the Champions League, and we will see during the season what we can do."
