Former Newcastle United boss Allardyce was in charge of West Ham for four years from 2011 to 2015.
During his time at the Boleyn Ground, the Englishman guided the London club to promotion from the Championship and established them as a Premier League side.
However, the football that the Hammers played under Allardyce was not pretty and did not go down well with the fans.
The former Bolton Wanderers manager recently told The Sun: “I once called the supporters deluded and I stand by that. I don’t know who invented the ‘West Ham way’ phrase, but it’s a millstone around the club’s neck.”
Former Wigan Athletic and Hull City midfielder Bullard, who did not make a single first-team appearance during his time at West Ham, has defended Allardyce’s claims.
“Big Sam has come out and called the West Ham fans deluded this week,” the 36-year-old wrote in The Daily Star. “I’m a big Hammer - and he's right!
“We're West Ham - not Barcelona - and we've got to realise who we are. We got Allardyce in to keep us up then all of a sudden West Ham fans want us to play quality football like Arsenal.”
Allardyce is a very good manager, and his work at West Ham should be respected. After all, the 60-year-old took the Hammers back to the Premier League and kept them there.
The problem was that Allardyce could not take the team to the next level, which is to complete for a top-10 finish on a consistent basis.