Pavel Pogrebnyak set Reading on their way after a Stephen Bywater howler just before half-time while Alex Pearce and Danny Williams added goals in the space of four second-half minutes.
The Royals' three goals at the Den took them to 15 from their last four matches, which includes a 2-0 defeat on the road at Ipswich this time last weekend.
Reading have now won four of their last five in the league, though, and boss Adkins believes that good form is down to him being able to pick the same team each week.
"We have come here able to select the same team for the fifth game running which helps and it was a great workmanlike performance," said Adkins.
"It was a typical Championship game. The lads worked extremely hard. There was a good shape about ourselves and we scored some good goals.
"You can see the togetherness of everybody which is great and it was a good three points at a very difficult place to come to.
"Everyone is working really hard, which has been demonstrated on a consistent basis for the last few weeks.
"Pavel has been top-drawer. He works very hard in training and just epitomises the way the team is at the moment.
"At times we have had up to 10 players injured so now it is really pleasing that we have been able to pick the same team for five games running and put a real consistent string of performances together."
Defeat was a first for Millwall at home under new boss Ian Holloway and he conceded the Lions played as if they were still being led by former manager Steve Lomas.
"That is obviously the feeling we have had here before I came and it is amazing how quickly it came back. I inherited a situation and I have got to make it better," said Holloway.
"For me I can take some important things from that. In life or football you cannot do anything without structure. We need structure. We need a phase one, a phase two and so on.
"I went to try and get back in the game and that is why the score became as bad as it ended. The longer you go without scoring a goal the more important the next goal becomes.
"I am happy to take it on the chin. We ended up with five strikers on the pitch and I will never do that again because we are not ready for that.
"Reading were better than us out there but they weren't three goals better than us."