The Whites collected all three points against the Lions to remain six points adrift of the play-off pack ahead of tough away trips to Leicester City and Crystal Palace, who both sit above Leeds in the table.
"We keep saying that it was a must win game and they all seem to be. All because we now have Leicester City and Crystal Palace away. They don't lose many at home and our away record is abysmal! So it was important to get three points on Saturday to keep us in touch," said the boss on the official website.
In the past few years clean sheets for United have been few and far between, but the Whites have yet to concede since shipping four against Man City in the FA Cup. It is crucial that defence remains solid for the rest of the season if Leeds are to mount a serious play-off push.
"We've now had three clean sheets in a row and are improving every game. Millwall was a tough game, and with the penalty save in the first half it made it even more difficult. You start thinking 'is it me?' At half time we had a chat and we all wanted to work harder to get the win."
The only goal of the game came from the penalty spot in the second half after Stephen Warnock took over penalty duties from Ross McCormack, who had a spot-kick saved in the first half, and fired home his first goal in a Leeds shirt.
"We didn't want Ross to take the next one, there is too much pressure on somebody when they have missed one," said the boss. "Stephen wanted to take it, he has taken a few and I don't think it bothered him.
"He has made such a difference to us at the back because he talks. Lee Peltier says he talks too much he drives him daft. To get that experience on the left with young Sam on the right, it's a great balance."
Despite the penalty miss, Warnock had words of support for McCormack, who was a constant threat to Millwall all afternoon, but narrowly missed out on getting his name on the scoresheet.
"It's not for the lack of trying," said the boss. "You don't miss penalties on purpose. He might just come good when we need it.
McCormack has failed to find the net for the Whites in the league since the Wolves game in February , but Warnock remains confident he will be back amongst the goals sooner rather than later.
"We haven't seen the best of Ross yet but he is still a handful."