Brendan Rodgers' side went back to the Premier League summit courtesy of a penalty in each half from captain Steven Gerrard.
The first of those came after Luis Suarez cleverly drew a handball from the otherwise impressive James Tomkins, but West Ham netted a controversial equaliser in first-half stoppage time.
Andy Carroll bundled into Simon Mignolet as the Liverpool goalkeeper dropped Mark Noble's corner for Guy Demel to equalise. Confusion reigned as referee Anthony Taylor overruled his assistant to give the goal.
Taylor once again put himself at the heart of the action by awarding the visitors a second spot kick, while television replays indicated West Ham keeper Adrian played the ball before bringing down Jon Flanagan.
"We wouldn't like to be talking about the decisions of the officials but unfortunately it seems to pop up rather too regularly for me," said Allardyce afterwards.
"We want to play a game of football and we want the team that wins to win through the way they've played, not through what decision the referee might have got wrong.
"Evening itself out doesn't work for me. Obviously there's two decisions today where one goes against Liverpool and one goes against us.
"That ends up with controversy, frustration and aggravation from the players losing their cool by the management of the players on the field by the officials not quite being up to the level you expect at this level we play at.
"The assistant referee has had a part to play as well today and, all in all, that's disappointing.
"As a performance we gave all we could give and tried our very best to upset Liverpool's winning streak, tried our very best to stop them getting their ninth win on the trot.
"Unfortunately for us they've won the game on two penalties rather than the attractive football that they normally play and create.
"The players have to take a lot of credit for that but we are disappointed that we haven't got anything out of the game."
