The Minstermen bossed the first half but failed to take advantage with Matty Blair and Michael Potts failing to convert good chances to hand their side an early advantage.
Keeper Scott Davies somehow turned Blair's effort wide and minutes later Potts should have put York ahead, somehow missing the target from five yards.
"I thought we were excellent," Mills said. "For 90 minutes we've had a good shape about us.
"We played well at Chesterfield and lost, we played well again today and our players were excellent.
"We've come here and got ourselves a clean sheet which I'm delighted about, it's a good point, it should have been all three.
"But if you don't concede you don't lose. All you can do is create chances and get into the position to take those chances.
"We haven't taken some opportunities which have come along, but I'm not going to knock my players because I thought we were excellent.
"I'm proud of the performance they have put in."