Elias Kachunga scored a dramatic stoppage-time winner and Wagner sprinted off to celebrate with his players.
Referee Peter Bankes sent him to the stands for the last few seconds as Wagner’s emotions got the better of him.
After the game Wagner said: “It is an emotional game and I lost control of my emotions.
“But I didn’t shout at anyone, or hurt anybody, but it is a rule that I must not leave my technical area.
“I have seen the referee and he will put that in his report.”
Wagner also spoke of his “anger” at critics who had questioned the character of his squad after back-to-back defeats against Sheffield Wednesday and Preston.
“I am angry that after two defeats I have to answer questions about the character of my players,” he said.
“At Huddersfield we are humble, we know where we come from. Eleven months ago I came here and I lost my first two games and we were in a relegation battle.
“Now we under-perform in one game against Preston and people question us. I am angry when I read that we need a new striker. That is not correct.”
Kachunga scored the only goal to spark wild celebrations in the third minute of added time when he headed home Harry Bunn’s cross.
Before then Derby keeper Scott Carson had pulled off great saves from Nahki Wells and Bunn and looked to have earned a point.
Derby head coach Steve McClaren admitted he had a big job on his hands at Derby
The former England manager said: “There’s a lot of issues, more than I thought there was going to be.
“We have some work to do on the training ground but we have to take heart and know we can compete in the Championship.
“The third game in a week is a test of stamina but there is plenty to do.”
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