The Tigers conceded after just 51 seconds as they were beaten at the KCOM Stadium for the first time since Adkins was appointed in December.
Hull sit just three points off the Sky Bet Championship relegation zone and Adkins let his players know how poor they had been.
‘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.’
Millwall took the lead when Hull missed a couple of chances to clear and Lee Gregory backheeled to an unmarked George Saville to score from close range.
Jake Cooper then headed in a second to give the visitors a 2-0 half-time lead.
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.’
Abel Hernandez, on his first appearance since August after overcoming an Achilles injury, pulled a goal back for the Tigers with 11 minutes left but Millwall held on to record a fifth successive away win in the Championship.
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.’
Preston are reportedly weighing up whether or not to make a fourth offer for Peterborough United left-back Andrew Hughes.
James Maddison has completed his move from Norwich City to Leicester City for an undisclosed fee.