The game was goalless after 39 minutes when the former England international brought down Kris Commons as the Derby forward attempted to go past him.
James escaped with a yellow card from referee Sheldrake, and to add to furious Derby boss Nigel Clough's frustration James comfortably saved Alberto Bueno's free-kick. City went on to win with two second-half goals from striker Brett Pitman.
"I haven't seen the incident again on film, but I thought we had a couple of defenders getting back to cover and that a yellow card was the correct decision," Millen said.
"I understand how Nigel feels and perhaps we got lucky. But I was delighted with the work rate of my team and once we scored the first goal I thought we went on to win pretty comfortably.
"Derby played a lot of neat football, but mainly in front of us without creating many chances. They did catch us on the break a couple of times, which was a concern, but overall we defended well."
Source: PA
Source: PA