The Cottagers came into Saturday's match hoping to repeat their away win over Norwich on Boxing Day and climb out of the relegation zone for the first time since early November.
But, after gritting out a goalless first half, the wheels came off in spectacular fashion after the break as Hull poured forward and found the net seemingly at will.
Having scored nine goals at home in as many matches, the Tigers took full advantage of some hapless defending and beat David Stockdale on half a dozen occasions in 35 minutes.
Any defeat can be hard to take for a side scrapping for their lives at the wrong end of the table, but this was Fulham's heaviest loss of the Premier League era and Meulensteen wasted no time in speaking to his players and drawing a line under proceedings at the KC Stadium.
"That is one of the things I addressed straight away in the dressing room: don't let this affect you in up and coming games," he said.
"We've got two crucial matches coming up and what we need to do is take it on the chin, learn from it and bounce back.
"We need to look back and make sure don't forget the good things we've tried to create over the last couple of weeks.
"We need to make sure sure we shrug it off and are ready to react against West Ham (on New Year's Day)."
By the time the Hammers visit Craven Cottage, Meulensteen can expect to have a number of first-choice players back in action having made six changes for Hull.
With just a day's rest between the Boxing Day card and Saturday's fixtures, Fulham were not alone in needing to shuffle the pack and the Dutchman was confident his chosen XI could take something from the trip.
"We always knew it was going to be difficult with two games in three days and you utilise your squad the best possible way you can," he said.
"Because of the intensity of games you are forced to make changes, with little injuries and niggles and that's why you have a squad.
"I was more than confident that the players I picked for this away trip were capable of getting a result and that is why it is so weird."
For Hull's buoyant manager Steve Bruce it was a joyous way to end a year that has seen him take the club to an unlikely promotion and make big inroads into keeping them in the top flight.
His side went 10th immediately upon the final whistle and Bruce admits the relative security of mid-table was beyond his own expectations at the start of the campaign.
"For me the bottom 10 teams are in it (a relegation battle). We're lying if we say we're not looking over our shoulders. Now we've gone top of that particular league.
"I didn't think it was possible but this is a great group of lads and they're desperate to do well."