The Baggies played some exhilarating football – and scored five goals – when they demolished Chelsea last weekend.
That was in contrast to what many people expect from an Allardyce side, with the 66-year-old labelled as a boss that plays direct football.
Allardyce, though, believes that perception is wrong and pointed to his hugely successful Bolton team – which included the likes of Jay-Jay Okocha, Youri Djorkaeff and Nicolas Anelka – as proof he is a manager who likes to play with a flair.
"Perception is very different to reality," the Dudley-born chief said. "I don’t like using the term fake news because it’s associated with Donald Trump.
"But the fake news in football is equally as fake as it is in politics.
"Perception is perception. It is not reality.
"I think too many people in the media and the fans with social media, live on perception rather than what the reality is.
"I don’t blame anyone for that because that’s the way of the world is.
"But the reality is look at my (Bolton) team and you tell me when I played (Jay-Jay) Okocha, (Youri) Djorkaeff, (Nicolas) Anelka, (Fernando) Hierro, (Ivan) Campo, Stelios (Giannakopoulos), (El Hadji) Diouf, (Gary) Speed – that we played like that."
Asked where the perception stems from, Allardyce – with a big smile – said: "It’s long old news, long old news.
"It started with jealous managers who we beat. (Rafa) Benitez when we beat Liverpool. (Arsene) Wenger when we beat Arsenal.
"It came from a lot of places and is ultimately going to be picked up by the media.
"I think another one was when we won the semi-final against Aston Villa – David O’Leary. Long old history.
"None of them are about anymore are they? There is only me. Here I am still batting away – over 1,000 games.
"And it’s lovely to see all you guys (the media) laugh in the background. Brilliant."
Asked if his overall aim is to have his team's playing the way Albion did at Chelsea, Allardyce said: "My teams play to the strengths and the abilities of the players we have.
"My pragmatic approach has always been – what are the players capable of?
"If that means we have to play a little bit less with how we get from A to B then we play that way because that is what they are capable of.
"I play, and I have always said this, winning football. Winning is the only thing that keeps you in job."