The Minstermen slumped to a 2-0 defeat at table toppers Harrogate - watch match highlights here.
The result leaves them in 7th although well adrift of Harrogate and Salford City at the top and Mills is fully aware that performances like Saturday won’t be good enough to challenge.
"I am disappointed to come anywhere and say that we were second best,” he said. “We know it's a local derby, we know what it's about. Unfortunately, it didn't happen for us and we were second best. That's a disappointing one.
"I am disappointed with both goals. Other than the goals, yes, they were lively and they won a lot of second balls - but they didn't really test Jon (Worsnop) with all the possession that they had.
"I will have a weekend that I am not going to enjoy because I have not won a game of football and particularly a local derby. But that comes with the territory. That's what the game is. What you do is bounce back.
Despite the gap, Mills knows it’s still early days in the title race. "I am disappointed that we are eleven points behind. I am disappointed that we have lost today," he added. "But we have got a long, long way to go. Football is a funny game and we have to make sure we bounce back, stick in there, keep working hard, and hope we can win enough games and the teams at the top drop a few. That's the game.
"We are in a situation we don't really want to be in. We are eleven points off the top," he reflected. "But that's where we find ourselves and we have to live with that, as we speak, and do something about it."