The Minstermen gained a comeback 2-1 victory after defeating Salford City thanks to two Jon Parkin goals in the second-half, writes Tom Feaheny.
Speaking to BBC Radio York, Mills spoke of how he was pleased with not only the win but the performance.
"We were the better team during the first-half, we were very good in the second, we played really well, and in terms of performance I will pleased with it all apart from 30 seconds where they scored.
"We showed a really good mentality to be a goal down against a good side and to get the win."
Mills believes this cup win adds to the momentum they have.
"It is now four unbeaten in a row, we have shown a great mentality to get back and pick up wins and also performances to boot as well."
Jon Parkin reached a landmark goalscoring wise, with Mills delighted for his striker.
"Jon get's his 200th goal and now 201 for him, he's had a tough time trying to get the ball in the back of the net to get that landmark, we are all really pleased for him.
"No matter what career you have, he has missed a few chances and it can get in your head, he knows he had to keep going, these goal will give him a lift."
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.