Southampton were the latest side to take all three points from Craven Cottage as their trio of England World Cup hopefuls put Fulham to the sword in the second half, with England manager Roy Hodgson in attendance.
Adam Lallana, once again the best player on the pitch, opened the scoring with a great finish before Rickie Lambert and Jay Rodriguez got in on the act.
The defeat leaves Fulham bottom of the table and, despite a busy transfer deadline day, which included the club-record signing of Greek striker Konstantinos Mitroglou, Meulensteen feels keeping the team in the top flight would be his greatest achievement to date.
"It is the biggest challenge I have ever faced in regards to being in football," he said.
"I think it is the biggest challenge Fulham Football Club has faced for many, many years. We cannot afford to lay down and feel sorry for ourselves and beat ourselves up about it."
The heavy defeat was made worse for Fulham with fellow strugglers West Ham, Cardiff and Sunderland all picking up victories, but Meulensteen was keen to remain focused solely on his own side's fortunes.
"It is very hard, but we can't rely on other teams," he added.
"It is about us, no matter what other teams do. The teams at the bottom work their socks off to get their points and teams like West Ham have a great week behind them.
"It is all about yourself - you can't look at others you have to look at yourselves and see what we can address."
Fulham matched Southampton during the first half, but the visitors stepped up a gear after the interval to run out deserved winners.
Lallana, Lambert and Rodriguez were able to once again showcase their talents to the watching Hodgson and Saints manager Mauricio Pochettino said they had impressed in recent weeks.
"If Roy Hodgson was in attendance at the games against Yeovil, Arsenal and Fulham he would have seen those three games live and in these three games those three players scoring goals," he said.
"It was very important that the three strikers got goals as that is always going to increase their chances of making it to Brazil - it was important for them."
The result follows from a 2-2 draw at home to Arsenal, Southampton coming out of a rut over Christmas, with Pochettino happy with the efforts of his squad.
"I think in that period we had quite a few injuries and players banned," he said.
"We are a very young team and don't have that many players within the team because that's how we want it.
"In a competition that is already months old it is normal that you will have ups and downs. We haven't forgotten the philosophy or the style of football we want to play, even if there have been ups and downs in that time and that has been very important for us."