Rotherham chief Paul Warne wished former loanee Tom Lawrence had stayed on the pitch as the Millers secured their third home win of the season.
“I don’t like playing against 10 men. The pressure is right off the opposition and they are free to express themselves and everyone does a little bit more. The boys withstood the pressure, though.”
Lawrence was shown a straight red in the 58th minute for a tackle from behind on Richie Towell.
Warne, who worked with Lawrence during the loan spell, added: “I know Tom really well and he doesn’t really play on the edge, he was more of a victim of circumstance. It was definitely a strong yellow and I can see why the referee has given it.
“At that time, it was a real hotpot of football. There were a lot of tackles flying around and yellow cards.”
The Millers’ winner came from Ryan Manning’s 63rd-minute penalty after Fikayo Tomori appeared to tangle with Kyle Vassell.
Warne continued: “The lads are doing really well. I know success is judged by points and I understand that but, for me, success is if they give absolutely everything and are the best they can be.
“Our performances this year have been pretty good – sometimes you get the rub of the green and we got that. Our keeper did not have a lot to do. He did not have numerous saves to make.”
Rams counterpart Frank Lampard says he will look back at the rulebook after he also saw red.
Lampard followed Wales international Lawrence out of the match in the 77th minute after he left his technical area to complain about a decision and he was swiftly dismissed by referee Peter Bankes.
The former England international said: “It was frustrating. Rotherham played well and deserved to win the game.
“We did not move the ball quick enough and the pitch did not help. We lost the game. We got a lot of things wrong. We didn’t play very well.
“I didn’t get a word from the ref. I need to go back to the rulebook myself because I do not want to be leaving the game. I was upset with a handball. If those are the rules, managers will get sent off every game.
“I like communication with officials but there was none of that.”
Rotherham United: Rodak, Vyner, Ajayi, Wood, Mattock, Vaulks, Towell (Palmer 86), Manning, Williams, Smith (Proctor 78), Vassell (Taylor 71). Unused substitutes: Forde, Price, Wiles, Jones.
Derby County: Carson, Bogle, Keogh, Tomori, Forsyth, Huddlestone (Holmes 73), Johnson, Jozefzoon (Bennett 64), Mount, Lawrence, Waghorn (Marriott 64). Unused substitutes: Wisdom, Roos, Ledley, Malone.
Referee: P Bankes (Merseyside).