City still tasted success against Arsenal last season, beating them 3-1 in the FA Cup in January.
Allardyce told The Sentinel: "You get more protective managers among the big boys.
"If you have caused an upset against one of them then the talk is about your style of play rather than the fact the other manager has technically and tactically outmatched them.
"An Arsene Wenger or a Rafa Benitez might say Stoke City are this, that or the other because they have been embarrassed by the technical and tactical awareness of the other manager. Unfortunately, those managers get listened to more than anyone else, it helps the media write stories and everyone reads that.
"Then it becomes a tag that you never lose.
"I had the same last season in our last but one game when we beat Arsenal 2-1 at Ewood Park.
"We picked out their goalkeeper as the weakest link so dropped every ball on top of him that we could and ended up winning 2-1 after scoring from two corners, but apparently you are not supposed to beat Arsenal that way.
"I am sure Tony Pulis would agree that we are employed by our clubs to do the best we possibly can for them.
"Tony has done a tremendous job to steer the club through two years in the Premier League."