Nigel Adkins felt the performance from his Hull side against Millwall was "a disgrace".
"That was by way and beyond the worst performance since I've been at the football club," he said.
"I need to get to the bottom of it. I thought we were a disgrace in the first half. It was a poor kick-off, they had a throw-in in their half and they go the length of the pitch and score.
"The first half was nowhere near the level that's expected and the level that the players have been producing on a consistent basis.
"I'm very annoyed, I'm trying to keep a calm voice for this, but I thought we were nowhere near what was expected."
Adkins took defender Angus MacDonald off at half-time. When asked why, the Hull boss responded: "I should've taken him off in the first minute. He was shocking first half.
"But I look at myself and the team selection. That was an area we knew we had to deal with and we didn't.
"I knew whoever played left-sided centre-back would have to head plenty of footballs and be competitive. Angus is very good at heading the football. But he wasn't today in the first half."
Millwall boss Neil Harris said: "The players were outstanding. Five away wins in a row is a big achievement for us.
"A lot of people wrote us off at the start of the season to be bottom of the league. To get to where we are 10 games to go is not a bad response from that team.
"I've just said to the players, 'I want 60 points as quick as possible. See where that takes us.'"
On the quick start, Harris added: "You don't get a much better start for an away team than that. I asked my players to impose themselves on the game and ask questions of Hull.
"It was a typical Millwall goal. Hustle, bustle, with some quality as well."
George Saville scored after just 51 seconds and Jake Cooper added a second before half-time, but the visitors were made to sweat after the returning Abel Hernandez pulled one back with 11 minutes left.
The Lions held on to extend their unbeaten league run to 10 games and hand Nigel Adkins a first home defeat in charge of Hull.
It took the visitors less than a minute to open the scoring. Jed Wallace picked up a loose ball on the right and chipped in to Lee Gregory, whose clever back-heel teed up Saville to slot in his eighth goal of the season.
Millwall did not sit on their lead and Tom Elliott, recalled to the side for the first time in a month, tested Allan McGregor with a fierce drive from the right of the area in the seventh minute.
McGregor also had to push away a snapshot from Gregory as the home crowd grew restless early on.
Hull gradually grew into the contest and had their first sight of goal in the 17th minute. Markus Henriksen delivered a fine cross from the left but Jackson Irvine steered his header narrowly wide of the right post.
They went closer four minutes later when Jarrod Bowen's spectacular drive from the edge of the area came back off the crossbar.
Kamil Grosicki was then denied by a fine sliding block from Mahlon Romeo before Sebastian Larsson fired over from a free-kick.
But 12 minutes before the break the visitors doubled their lead when Cooper, on his 50th Millwall appearance, looped a header over McGregor from Ben Marshall's corner.
Hull looked to hit back before half-time but Ola Aina could not keep his shot down after the ball dropped to him on the edge of the box following a Larsson corner.
In a quiet start to the second half, Bowen shot straight at Jordan Archer before Gregory forced a similarly comfortable save out of McGregor at the other end.
The home fans found their voice when Adkins brought on Hernandez before the hour mark. The striker had been sidelined since August with an Achilles injury.
And with 11 minutes left he brought the game to life with a close-range finish after fellow substitute Harry Wilson's left-wing cross found a way through the box.
Hull pressed for an equaliser in the closing stages, firing a barrage of crosses into the visitors' area, but Neil Harris' side held on through five minutes of stoppage time to continue their run.