First-half goals from Elias Kachunga and Nahki Wells either side of former Town striker Danny Ward’s neat finish gave Huddersfield a fifth win from as many games at the John Smith’s Stadium this season.
It could have been different for Huddersfield had an unmarked Tom Adeyemi headed home rather than wide five minutes from time but despite that late scare, Wagner was in no doubt that Town were worthy of the victory.
“I think we totally deserved the win tonight,” he said.
“We deserved it because we played a fantastic first half, especially defensively. We were very hungry, aggressive and we didn’t give them any turns in our fighting zone.
“Unfortunately we were a little bit sloppy in the final third and we had to be more than one goal up because they had one situation and scored. We found a good answer with Nahki’s goal.
“In the second half everybody was able to see how strong Rotherham are, especially in their offense. They have some high-quality players that can cause you some problems.
“They did that but because of the togetherness, fighting spirit and work ethic in the second half and the good first half, we deserved the result.”
Town replaced Norwich at the summit ahead of the Canaries’ clash with Newcastle on Wednesday but Wagner is aware how quickly things could change in the Championship.
“We’ve now won five out of five very tight home games so everybody knows to be focused in every single situation to get us over the line,” he added.
“I think now we can say after seven wins out of 10 we’ve had a very good start.
“But it shows how tight this division is that we are only winning or losing by one goal.
“You always have to be switched on and work every single game very hard to get a result.”
While Huddersfield continue to grind out results, Rotherham sit at the foot of the table without a single point on the road and with only one victory in all so far this campaign.
“It is easy for us to feel sorry for ourselves,” said Millers manager Alan Stubbs.
“It was one of our better performances away from home, there was no denying that, but we’ve come away with nothing.
“The team showed a lot of character but there are small margins between a dozen teams in this league. We need to help ourselves.
“When results don’t go your way it does affect confidence - you take an extra touch or you’re extra cautious.
“I can see that in our play but we have to believe in ourselves.”