Having been relegated after only winning seven games across their last Premier League season, a poor start to this campaign - when they went six games without a win - had people writing off the Cottagers immediately.
Parker was well aware of the "narrative" around his side earlier in the campaign and says recent performances have changed people's perspective of the west Londoners.
There have still only been two League wins this season, though one came at high flying Leicester while Parker's side have also taken points from Liverpool, Tottenham and Southampton in recent weeks and could well have got something against Chelsea last week.
"We've done remarkably well considering where we were at the start of the season," said Parker. "We were probably a laughing stock in terms of how people were portraying us. But never was that the case in house, never was that the case from myself or the players.
"It was clear, wasn't it? There was a narrative around us at the start of the season, a narrative that was helped by our previous time in this division. We lost two games by more than two goals and that narrative was instantly in people's heads. 'Oh look, it's the same Fulham, that's what's going to happen this time around.'
"People were blurred a little bit by what happened the last time we were here and I can understand why. It was certainly an area we needed to address to have a chance of doing well. It was clear, everyone was along the same lines, that it was going to be tough for us.
"We've done remarkably well to be able to fight and punch our weight. We're not just doing it with determination and grit but with a real style about us, and it's clear people can see a real drastic improvement in our game. But it's coming down to results now. We've got a lot of draws and we need to turn them into wins to stay in this division."