The Minstermen manager is a firm believer that sides raise their game when they visit.
So despite Trinity's lack of form going into the Vanarama National League North encounter, Mills has fired a warning to his players not to take them lightly.
York have beaten Stockport County and Spennymoor in their last two games and that has raised spirits after a mixed August.
Mills knows everyone will be expecting a home win tomorrow but has urged caution, saying: “Teams get a lift coming here and that’s why you get shocks in the FA Cup.
"All the players at this level have the ability – it just comes down to having the mental strength to perform to the best of your standards every game.
“Gainsborough will come here and treat the game as a cup final and we will need to be at our highest level because, if we are, we will still beat them.”
The manager told the York Press that the match tonight may be won in the mind.
“I’m not worried about the players’ ability, but we have to make sure we’re mentally right for every challenge that is put in front of us,” Mills said.
“On the back of two wins, we will have a different mentality to that we had after back-to-back defeats, but we can’t get complacent."