Pellegrini told reporters after the game: "West Ham played very well and with a very high intensity. We had a lot of chances to score but it is difficult to win if you don't take them.
"I don't think it was a fault of our team for the performance in the first half, it was more about the intensity of West Ham and you must credit them for that.
"We are just starting the season, we have 80 points left to play for. So it is early. We will continue fighting because there is no title being handed out at the moment."
The result means that Man City are third in the Premier League table, on 17 points.