Matty Blair gave the Minstermen the lead in the 63rd minute but Rotherham pulled level in the third minute of added time when leading marksman Daniel Nardiello equalised from substitute Ben Pringle's cross.
Mills said: "Our shape, our discipline and our quality was excellent. It's a hard one to take, but it's just the way it is going for us at the moment.
"You see five minutes going up as added time and in that time they got their goal. We are looking at things we could have done to avoid it, but it's happened now and it's a draw away from home. Maybe before we would have taken that.
"I thought we were different class to Rotherham tonight. I thought we played superbly well and it was an excellent performance.
"We haven't got what we deserved tonight and that was a win. We deserved to take the lead and we had two or three other chances which we did not take. We go away disappointed."