The Hammers started their Premier League campaign in the worst possible fashion, falling to a 4-0 loss away to Liverpool on Sunday afternoon.
Pellegrini was unhappy with the officials' decision to let Sadio Mane's second goal stand, with the Senegalese forward well offside, but the Premier League title winner concedes that a vast improvement is required at the London Stadium in six days' time.
"We knew before the game that our start was very difficult. In our first few games we need to play some of the big teams," he told BBC Sport. "It's difficult to play when you concede four goals. We started the second half and the referee didn't see a clear offside.
"We need to win our second game. We need to work during the week and try to win three points at home. We not only have nine new players, but three or four players who were not completely fit in pre-season. We need to improve in attack and continue working. I am sure next Saturday we will see a team that is trying to win."
Pellegrini has lost more Premier League games against Liverpool (5) than he has against any other opponent in the competition.