The Minstermen sit in ninth in the table after losing for the second time in a row, writes Tom Feaheny.
Speaking to BBC Radio York ahead of their away trip to the North-East, Mills said.
"I've been in football long enough to know you can have a poor week then have a good one to rectify it, we know that Spennymoor are on a good run, it's a tight ground, we want to have that new week now and get that win.
He added: "There are nine points at stake in the next week we get them, we are back in the top seven and moving up the table quickly, but we know we have to go and do that."
The York boss believes that their response is now crucial.
"I think Saturday we deserved to lose, the other games, it's just a case of not taking chances, we just now have to respond. We've played eight games, we would rather have a few more points on the board but the next three games will tell me a lot."
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.