The Hammers eventually lost 2-1 to the league leaders at home but not before some controversies throughout the 90 minutes affected the result.
The Reds received a penalty in the 44th minute for a handball against James Tomkins, which was dispatched by skipper Steven Gerrard, before Guy Demel responded when Andy Carroll appeared to impede visiting goalkeeper Simon Mignolet at a Mark Noble corner.
With just under 20 minutes remaining, referee Anthony Taylor awarded another penalty to Liverpool when Jon Flanagan went down under pressure from Adrian who did make contact with the ball.
Gerrard again converted, and although the decision was questionable, Allardyce was proud of his players for the way they soldiered on against a top quality opponent.
"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," Allardyce said.
"We gave all we could give and we tried our best to upset Liverpool's winning streak and to stop them getting their ninth win on the trot.
"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."
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