Meulensteen's side remained solid enough in the first half at the KC Stadium on Saturday and aside from seeing a Tom Huddlestone free-kick hit the post, goalkeeper David Stockdale was given mostly routine saves to make against his former club.
The second half was a completely different story, however, as Hull plundered six goals. Ahmed Elmohamady, Robert Koren, George Boyd and Huddlestone put Hull 4-0 up by the 68th minute, but worse followed for Fulham, who are in the bottom three.
Matty Fryatt added a fifth before Koren grabbed his second of the day to leave Meulensteen dumbstruck by his team's performance and the result.
He said: "I've asked myself and I've asked the players, but it's something I didn't see coming after the good result against Norwich.
"But we lost easy possession in the middle of the park which resulted in a corner four minutes into the second half and they scored.
"Okay, it's not the ideal scenario but to not get back into the game at all and concede three goals in about seven minutes isn't good.
"In some of my other games in charge we didn't get the result our play deserved.
"This obviously doesn't fall into that sequence. Losing is hard to take, but losing in such a manner is hard for any professional. We need to make sure we don’t look back, shrug it off and be ready to react against West Ham on New Year's Day.
"It's one of the things I addressed straight away in the dressing room. Don't let it play on our up-and-coming games. We have two very big matches coming up.
"The important thing is we take this on the chin, we learn from it, we bounce back from it and we react.
"But I'd also like to issue an apology to the travelling fans."
Meulensteen made six changes to the team that beat Norwich City at Carrow Road on Thursday, but he does not believe rotation is to blame for the defeat, insisting that during the hectic festive period such measures are essential.
He added: "We always knew it was going to be difficult with two away games in three days.
"We utilised the squad the best we could and I was more than confident that the players I picked were more than capable of getting a result.
"Sometimes because of the intensity of games, you're forced to make changes due to little injuries and niggles and that's what you have a squad for. After our previous performances I just didn't see that coming."
