The Hammers manager insisted that he had told his players to expect an emotional home crowd to get behind Everton, and believed that his players had not performed to their ability.
Allardyce admitted that West Ham were lucky to lose by just two goals after goalkeeper Jussi Jaaskelainen made a string of fine saves to deny Everton during a ninety minutes in which the away side failed to get a foothold.
"The way we played today we were lucky to get away with 2-0," Allardyce said.
"There was only one player who has been outstanding for us and that was (goalkeeper) Jussi Jaaskelainen who made some outstanding saves.
"I warned the players before the game what it was going to be like - it was exactly that and the players couldn't cope."
West Ham are yet to cement a top-half finish going into the final game, and face relegated Reading on the final day.