The Hammers looked to have turned the corner on their own turf after comfortably beating Fulham last time out.
However, after another below-par attacking display, the Upton Park faithful let their feelings be known at the final whistle, with the players exiting to a chorus of boos.
And Allardyce knows where the supporters are coming from, and believes the fans are right to vent their frustrations.
"It doesn't make it easier for me, but it is part of the job," he told Sky Sports.
"You sit there and you expect that reaction when your team doesn't perform.
"We didn't entertain them and, more importantly at the moment, we didn't win."
Allardyce, who celebrated his 100th league game in charge of the Hammers, has seen side win only two of their last 15 league games, and knows things must improve quickly, and return to the form his side showed against Fulham.
"We didn't do what we did against against Fulham, which was a brilliant game," he added.
"Today dogged hard work was the order of the day, and we didn't deserve more than a draw."