The Hammers prop up the Premier League table after the opening matchday following their heavy defeat on Merseyside, with Mohamed Salah, Sadio Mane (2) and Daniel Sturridge getting the goals for the home side.
Pellegrini acknowledged that Liverpool were the better team and deserved their victory, but believes that the final scoreline was harsh on his side.
"It was a tough game before the game, during the game and after the game. We knew we played against one of the best teams in the Premier League. They reached the final of the Champions League and bought a lot of new players. We knew it was going to be difficult," he told reporters.
"I think Liverpool played better than us. They deserved to win. When you lose 4-0 you cannot have excuses. But I think a couple of balls decided the score. In the first half we had two or three clear chances to make it 1-1 and we conceded the second goal in the last second of the period.
"The after that a clear offside goal decided the game and they had a lot of confidence to play at 4-0. I am not complaining. Liverpool played well, but I don't think the difference was four goals."
West Ham's second match of the season comes against Bournemouth next Saturday.