City are also the only club this season to have not conceded a single goal in their campaign.
The club, who finished eight points behind Chelsea last season, have already been tipped as favourites to win the title but Pellegrini said such talk was premature.
"We are very pleased with the start but we are not thinking about what we are going to do at the end of the season," the 61-year-old Chilean told the club's website.
"The highlight was the way we played. It's important to continue the style of football; the team won the four games in the way I like to play.
"If we think that because we won the last four games we are going to win the next one, we are going to make a big mistake."
Swansea's Ayew, who arrived on a free transfer, has made a fantastic start to life in England, scoring three goals and provided an assist in four games.
The 25-year-old Ayew thanked the whole team for the award.
"It's a great feeling, but this award comes from hard work and support by the whole squad," the former Marseille winger told the Swans' website (www.swanseacity.net).
"It's more of a collective award rather than an individual award because we've worked very hard from pre-season until now."
(Reporting by Shravanth Vijayakumar in Bengaluru)
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