The West Yorkshire side were coasting at half-time as, playing against 10 men, they led 2-0 through goals from Chris Wood and Souleymane Doukara.
However, they took their foot off the gas after the restart and had to endure a nervy final 10 minutes when Millers captain Richard Wood headed home, with Dominic Ball going on to miss a sitter shortly after.
Leeds held on, though, to beat Rotherham in the league for the first time in 34 years and move back into the Sky Bet Championship play-off positions.
“We brought it on ourselves,” Monk fumed. “We warned the players at half-time about taking our foot off the gas and that’s what we did.
“Overall we were worthy winners, no one can doubt that. The first 25 minutes was excellent, we got ourselves into a strong position.
“The only thing that could hurt us is taking our foot off the gas.
“We are not good enough to play anything less than 100 per cent, especially in the Championship.
“Overall we are happy with the three points, we deserved the three points, but it is a lesson learned.
“Good teams sense blood, they don’t let the rope loose, they go for it. It could have easily turned into something worse than what it was.
“We were trying to force it too much, we played into their hands. It needs to be a lesson learned. We should have put the game to bed.
“I’m happy with certain aspects, but disappointed with others.”
Rotherham, who are 11 points adrift of safety and winless in 14 games, endured a nightmare first half as they conceded two goals, saw Peter Odemwingie sent off for a shocking elbow and lost Lee Camp and Greg Halford to injury.
But in the second half there were positives to take and they almost snatched an unlikely point.
“There was a younger group on the end and they showed heart, running and quality and no little ability and I am very pleased about that,” said boss Kenny Jackett.
“It could have got us back in a game that we looked out of. They are the future and something we can build on. We have to show that sort of commitment. They have to show that enthusiasm and willing in every game.”
On the first-half sending off of Odemwingie, Jackett added: “Peter has put his arm up to protect himself. I can see why the referee has done it, I don’t think we can have any complaints if he has seen that way.
“Peter is not an over-aggressive person or malicious, but he has put his arm up to protect himself. It looks how it looks, I understand the referee’s point of view.”