Monk's promotion-chasers were lucky to go into the half-time interval on level terms after the rock-bottom Millers were the better side in the opening 45 minutes, before Kyle Bartley's header and Chris Wood's double earned what turned out to be a comfortable 3-0 win.
But Monk was not pleased with the first half and a better side than League One-bound Rotherham would have made his side pay.
"The first half was as poor as I have seen us for many months," Monk conceded.
"It was classic from the away team, trying to slow things down, we were playing into their hands.
"There was no aggression, no intensity, no urgency, we were very lucky to come through unscathed. There were a few choice words, we made a change and it had an effect on us.
"The second half was a very good performance, much more like ourselves. No disrespect to Rotherham, but when we play better teams we will not be afforded the luxury of playing like that.
"We have to be at 100 per cent, we cannot afford to be below 100 per cent. Three goals and a clean sheet, you have to be pleased in the end."
The second half was a completely different story thanks to Bartley's early header, powering home a corner, and then Wood's double made the game safe. The first was a superb individual goal and the second a neat finish from close range.
The win keeps Leeds locked in the top six and they are dreaming of a promotion push in the second half of the season.
Rotherham look like they will be leaving the Championship at the other end of the division after they sunk to a 17th defeat of the season when they could not capitalise on their first-half dominance.
Caretaker Paul Warne said: "I thought we were excellent in the first half. I came to win the game, these are great places to play.
"To go in 0-0 was a bit of an injustice for us. We created loads and I was enjoying the game, I enjoyed the way we played. Half-time came and I knew it didn't count for anything.
"To concede from a corner was disappointing and it was a blow for my players and they didn't deserve that.
"That first goal changed the game.
"They get one or two chances, they score, we get one or two chances and don't score. From box to box we were excellent. The fine margins at this level and the quality are going against us."