The Dutchman, who replaced the sacked Martin Jol at the start of the month, made six changes to the side that won 2-1 at Norwich City on Thursday and the move backfired as Robert Koren (2), Ahmed Al-Muhamadi, George Boyd, Tom Huddlestone and Matt Fryatt struck for Hull.
"The important thing is we take this on the chin, we learn from it, we bounce back from it and we react," Meulensteen told reporters.
"I'd also like to issue an apology to the travelling fans. It's something I didn't see coming after the good result against Norwich.
"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, we shrug it off and be ready to react against West Ham United on New Year's Day."
Meulensteen said he rotated his squad due to the congested programme of fixtures over the festive period.
"We always knew it was going to be difficult with two away games in three days," he explained. "We utilised the squad the best we could and I was more than confident the players I picked today 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."
Hull manager Steve Bruce was almost in shock after his promoted side chalked up their biggest Premier League victory.
"It's quite incredible really," said Bruce. "The first goal goes in and then all of a sudden the floodgates have opened which doesn't happen very often at this level - I can't remember ever having an afternoon like it.
"We've now scored eight goals in two games here, it doesn't make sense. This was one of the great days we will remember for a long, long time," said the former Manchester United defender.
Bruce singled out midfielder Tom Huddlestone, his close-season signing from Tottenham Hotspur, for special praise.
"I don't often pick out individuals but I don't think I have witnessed a performance as good as what I have just seen from Tom Huddlestone," said Bruce after Hull climbed to 10th in the table. "He gave a masterclass of how to play in midfield.
"The free kick he hit in from 40 yards, there are not many people who can even try to strike from there. He's an outstanding footballer, everything he did was effortless."