The Chilean took over at City in July following the sacking of Roberto Mancini after the club finished last season without winning a trophy.
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"I think we have the best squad in England,” said Pellegrini, speaking at a question and answer session with supporters on Thursday.
"We bought four important players, we already had a very good team and with these four players I think we improved a lot.
"We hope that from the first match against Newcastle at home we will start winning, and we will try to bring another trophy here."
City host Newcastle on August 19 before facing newly promoted duo Cardiff and Hull City on August 25 and 31, respectively.