"We are trying to change our mentality. Last season we tried to play on the counter-attack and this year we want to have more minutes in the other team's half with the ball," Pellegrini told reporters ahead of Saturday's home match against Bournemouth.
"Every week is important when you bring so many players in and make so many changes. You work on your team and every week it can be better," said the Chilean, who replaced David Moyes as manager in May.
"Every fan demands the best from their team. The West Ham fans always support us. Sometimes they have more patience than other times, but all fans demand good results."
Pellegrini backed new signings Felipe Anderson and Andriy Yarmolenko to add flair to team.
"Anderson is a fast player, a mix between a winger and a midfielder, and I think players like him and Yarmolenko will bring a lot of creativity."
Bournemouth began their campaign with a 2-0 victory over promoted Cardiff City last weekend.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Mark Heinrich)
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