An under-par United won thanks to two Paul Pogba penalties, returning to winning ways after back-to-back defeats.
But the decision to award United their first penalty – when Robert Snodgrass was deemed to have fouled Juan Mata – was contentious, and West Ham should have taken the lead in the ninth minute but Felipe Anderson’s goal was incorrectly ruled out for offside.
Pellegrini also said United’s second penalty should not have stood because Anthony Martial, who was fouled by Ryan Fredericks, was offside in the build-up – although replays seemed to show he was onside.
“I am not complaining about the referee because they were not big mistakes, difficult mistakes, but with technology we have a different score,” Pellegrini said.
“Felipe Anderson was onside. It was not a penalty from Robert. The last goal from Man Utd was offside, the last pass.”