The Hammers should have been in front in the first half when Michail Antonio, in for the injured Marko Arnautovic, misfired down the left before seeing a close range effort clawed away at the near post by Kepa moments later.
The best chance of the game, though, fell to summer signing Andriy Yarmolenko. The Ukrainian, who announced his arrival in the Premier League with two goals at Everton last weekend, was left alone five yards out at the far post when he met Robert Snodgrass’ cross, only to inexplicably head wide.
While a point against the division’s early pace-setters is a good result for this West Ham side, the Chilean was left frustrated at not claiming consecutive wins.
“When you have such clear chances against big teams you must score one of them,” Pellegrini said.
“We had three clear chances before they created one chance, you must score... you don’t deserve to score, you must score.
“I was not happy with the way we kept or had the ball in the second half, the first half was clear the way I wanted to play, the second maybe we lose too many balls.
“Against these teams if you cannot win, don’t lose it so I think the draw is not a bad point but always thinking that with those chances we could have had three.”