"If we take them, we win the game" - Millington rues missed chances after Shaymen forced to settle for a point by York's late equaliser
"It was probably a fair result on the balance of play," the Town boss told the Courier.
"We shaded certain aspects of the game, we had more chances, we had more shots.
"All in all, it felt like a local derby, certainly as the game wore on, it became a bit fraught and a bit frenetic and a bit direct.
"Neither team really controlled it for any real length of time, so all in all, we've got to be happy with a point."
Asked if the draw felt more like a defeat in the circumstances, Millington said: "No, not really. A point away from home is always a positive, especially in a local derby, because they can go either way.
"I think the disappointment for us is more around our failure to control the game once we went 1-0 up.
"We were quite comfortable in the game up until that point, and even after that we've created a couple of real clear-cut chances that we failed to work the keeper.
"Flo Hoti scored an absolute worldie to put us 1-0 up but then misses a much easier chance a few minutes later.
"Milli Ali's worked incredibly hard today and not had much opportunity and then the opportunity he gets, largely created for himself, he puts it way over the bar.
"These are the differences between the teams who are going to be in the top three or four places and the rest.
"If we want to be really punching at the top end of the division we've got to take those chances.
"If we take them, we win the game two or three nil quite comfortably and I think York probably struggle to muster a response, but we failed in that and as a result, we gave them an opportunity."
On whether he was disappointed by the manner of York's equaliser, which came from a long ball upfield that Town failed to deal with, Millington said: "I think that's the nature of the league isn't it, you're always at risk when teams go long, especially late in the game when there's fatigue, which is possibly an issue for us at the moment because of the amount of injuries we're carrying and having to roll out the same team week-in, week-out for the last few weeks.
"Anybody who knows the league knows you can be vulnerable to that late on.
"Were this game on Tuesday instead of today, I think we would have won it because we'd have had that little bit of extra energy in the legs and we'd have been able to go that little bit harder in the key moments.
"But the lads have given everything in the last few weeks and it may be a bit greedy of me to expect them to go on and see off a team who are fighting for their lives at the moment and trying to build a run for themselves."
Millington was back on post-match media duties after not speaking to the press following Town's last two games.
"Just trying to focus my energies as much as possible on making sure the lads are fully prepared and ready to go," he said when asked why.
"Although the media obligations are an important part of modern-day football management, sometimes it can take over and distract from what is the core of the job, which is preparing a team to try and go out and get three points."