The Minstermen were five minutes from victory at Martin Allen's automatic promotion-chasers after Patrick McLaughlin's second-half corner was diverted into his own net by Gills defender Charlie Lee.
However, Cody McDonald salvaged a point for the home side with an 85th-minute header.
"It was a very good performance," Mills said.
"We went down there and played our game really. We played extremely well.
"We had chances to win it and hit the post when we were 1-0 up and they scored late on when I thought we were going to hold out.
"We've done very well in a short space of time. A year ago we were nowhere near coming to places like Gillingham. They're a big club with a relatively big budget, but we've gone there and been the better side.
"We dealt well with balls into the box. We're not the biggest side, but we showed we're hard to beat and when we were in possession we passed it the way we like to."
Mills' side return to Bootham Crescent on Saturday against Morecambe when they will be looking to secure their first home win in three.
"We've done extremely well on the road this season," Mills added. "We've won four and drawn eight away from home.
"Quite a few of those, and a couple at home, we've drawn when we could quite easily have won. But it's not quite happened for us at home."
