Steve Bruce’s men six second-half goals to ensure Fulham remain in the Premier League’s relegation zone.
“An apology for the travelling fans is right in this place,” Meulensteen told BBC Sport.
“I’m shocked. I don’t know if there was something in the tea. Today was just not good enough.”
It was Fulham’s fourth defeat in six matches under their new manager, who took over from the sacked Martin Jol.
Meulensteen’s men will host fellow strugglers West Ham and Sunderland in their next two league games, with an FA
Cup third-round trip to Norwich separating the crucial fixtures.
Any optimism derived from their 2-1 league win at Carrow Road on Thursday was extinguished in a hapless second 45 minutes at the KC Stadium and they have now conceded 41 goals this season, including 15 in their last four games.
“I did not see that coming and the players did not see that coming,” added Meulensteen of the 6-0 hammering at Hull.
“We didn’t play particularly well in the first half but were still in the game. The spell from 60 minutes onwards they
scored three quick goals and it was game over. We couldn’t come back from it.
“I thought [the game] against Norwich was much better, but today wasn’t and we need to go back to the drawing board.”
Meulensteen, who made six changes for the game, said he took “full responsibility” for the defeat but urged his players to bounce back on New Year’s Day against West Ham.
“We can’t get too down about it, there was improvement against Norwich but today was not acceptable,” he said.
“We have to make sure we react, so in that way it’s good we have another game so soon.”
Midfielder Steve Sidwell echoed his manager’s sentiments.
“To concede six goals was unacceptable,” Sidwell told BBC
“It hurts for us playing it, it’s hard for the fans. [From} all of us in the dressing room we apologise to the fans who
travelled up to see us at a difficult time of the year.
“The best thing to do is analyse it, put it to bed and prepare for a a big game coming up.
“They’ve seen in recent weeks that our performances have shown under Rene that we have desire and passion and the result against Norwich showed that.
“[Hull] was a bolt out of the blue and hopefully it won’t
happen again. It was unacceptable.”