Despite having a number of chances in the first period, the Minstermen failed to find the net and have now failed to scored on home soil in four successive matches. Goals from on-loan strikers David McGoldrick and Callum Ball, an own goal from Jamal Fyfield and left-back Chris Hussey's surging effort gave the Sky Blues a comfortable win.
"It's ridiculous," Mills fumed. "The first two goals and the third goal, I can't believe what I've watched. I really can't believe what we've given away. We've come out and not really started the second half and they've pushed us straight away.
"We've given them three goals to lose. When we don't have a good start to the second half we must remain solid and keep doing the right things, and we didn't.
"I thought we were excellent in the first half without taking the chances again to go and score. I think it's the fourth game in a row we've not scored a goal at home, so obviously that's a concern. We've created numerous chances but just not put them away.
"We've just given goals away here, I can't say anything more than that. We've just put them on a plate for them and that's the end of us in this competition. It hurts. I'm gobsmacked how you can play like that in the first half then play like that in the second half."