Allardyce has said that he was disappointed with the performance of the officials after three controversial goals were awarded during the match.
"Obviously there are two decisions today - one that goes against Liverpool and one that goes against us and that ends up with controversy, frustration, aggravation and the players losing their cool," Clubcall.com quotes him as saying.
"Unfortunately they've won the game on two penalties rather than their attractive football that they normally play.
"The players have to take a lot of credit for that but we are disappointed we didn't get anything out of the game."
West Ham return to action against Arsenal on April 15.