The Hammers were without Andy Carroll due to the terms of his loan deal but Carlton Cole performed admirably in the loan striker role.
Both teams had chances to win the game but West Ham goalkeeper Jussi Jaaskelainen was again in fine form saving well from Phillipe Coutinho and Daniel Sturridge.
The Hammers had a chance to steal all three points at the end of the game when a Jack Collison header was cleared off the line by Liverpool midfielder Lucas.