A banner unfurled during last weekend's 1-0 defeat to relegation-threatened West Brom declared a certain number of Hammers supporters were keen for owners David Gold and David Sullivan to replace Allardyce.
The 59-year-old was also given little backing in an online poll conducted across independent fans' sites, with over three-quarters of respondents wanting to see the former Bolton manager's 35-month tenure at Upton Park brought to an end.
Many have cited negative tactics as the reason for their unrest, but Allardyce believes a recent barren run of results has seen some fans turn on him - claiming a 0-0 draw at Chelsea, which saw the Blues have 39 shots to West Ham's one, was celebrated as a triumph despite Jose Mourinho describing it as "19th Century football".
"It is a nonsense," said Allardyce of the fans' criticisms.
"Their perception is because we haven't won (in four games).
"When we went to Chelsea and they were all very, very happy that was based purely on a well-structured defensive ploy with little or no football at all
But it was still hailed as a great performance.
"You can't expand and open up against Chelsea because you lose five or six-nil
We play to win when we play a game and if we don't play to win we play not to lose
Our biggest problem is that we haven't drawn enough in between the wins."
Allardyce welcomes Tottenham to Upton Park in Saturday's early kick-off looking to record a third victory of the season over their London rivals.
Following a 3-0 Barclays Premier League win at White Hart Lane in October, Allardyce's side repeated the trick when they came from behind to secure a 2-1 victory in the Capital One Cup quarter-final.
Spurs head coach Tim Sherwood also faces an uncertain summer, with reports continuing to appear that the club are lining up a replacement for the man who took over from Andre Villas-Boas in December.
Allardyce accepts that constant speculation and pressure on managers is part and parcel of the modern game as he tried to shake it off and focus on improving on the Hammers' poor form.
"No one wants to see things like that (the banner at West Brom) and wants to be criticised," he added.
"It is what it is at the moment
It is part of the job today and altogether people keep telling me how to play and the performances we need to give.
"In our last four games our performances have been good, but without a result comes the criticism
It is about results, not what you have done for the 90 minutes, it is what has come out of the end of it.
"Of course it (criticism) bothers you but you don't let it affect your clear thinking
You concentrate on the players and make sure they continue to strive to get better and better.
"This year, while the league has been extremely entertaining, we have had ups and downs
It has been a pretty hectic season, a pretty demanding season for us all, and I think that is shown in the fact that 10 managers have changed in one season."
Source : PA
Source: PA