Jamie Stott was sent off on his debut either side of an early goal from Ephron Mason-Clark and a late goal by Nicke Kabamba.
"Very disappointing," said Millington. "We always go out to win every game, but we'll take a negative result when we've performed well or at least tried to perform the way we want to.
"And I don't think there were enough players at it today. The reason behind that I couldn't necessarily say at the moment, but I will look into the performance and draw my conclusions from that."
When asked what had disappointed him most about his team's performance, Millington said: "It was the lack of our identity really.
"First and foremost we've got to be willing to go and earn the right to play, we've got to win more headers, we've got to win more tackles, we've got to land on more seconds, we've got to carry more of a threat going forward, we've got to be willing to stay on the ball in their half.
"All of those things weren't present and without those, then we can't display any of our identity.
"That's the big frustration because the lads have worked so hard to develop that and yet today, almost none of it was on display."
Millington admitted his side's poor performance took him by surprise.
"As a group of players and a group of staff, we were confident that the performance would be at a better level today," he said.
"We knew what Barnet would bring to the table, they did exactly what we expected and they did it very well. They'll cause a lot of teams a lot of problems this season when they play like that.
"But certainly we weren't expecting what we got from our team today."
Millington added: "We've discussed it, one or two of the players have offered their thoughts and we're all in a agreement that it's putting the basics right first, and then we can be a little bit more detailed in our play, we can show more of an identity, we can show more of our tactical nous.
"But the basics have got to be there first and there weren't enough players putting the basics in place today for us to be able to show what a Halifax Town team is."
On Stott's sending off for two bookings, Millington said: "Jamie's got to take responsibility for that and it's going to cost us.
"But the inconsistencies that came out in some of the decisions was frustrating because I felt that there were very similar decisions that Barnet simply weren't penalised for.
"There was an almost identical situation just a minute or two before on the opposite side of the pitch that was let go, and then we were penalised with the situation with Jamie, which is frustrating."
Millington felt his side could have got something from the game had Stott not been dismissed.
"I think we were starting to compete in the second-half more and we were creating more opportunities," said the Town boss.
"I feel we would have had a much better chance of getting something out of it had we had 11 men, but we didn't deserve anything out of it on today's performance, so we can't grumble at that."
Matty Warburton missed the game with a calf strain, while Jesse Debrah was absent due to a quad strain.
"We made the decision to be careful and not risk them at this early stage," Millington said.
"Kian Spence is still on the road to recovery but very close to being available, if not for Torquay then I would hope Southend."
On other absentees Festus Arthur and Angelo Capello, Millington said: "They were just unfortunate that they didn't make the squad, but they've trained very well and they're certainly doing everything they can to stay in my thoughts."
And on the new signing Town are in the process of completing, Millington said: "I'm sure it will happen but it's just a slow process."