Devante Rodney had put Halifax ahead against his former club, but Luke James equalised for the hosts.
Lee Molyneux then scored what proved to be the winner shortly after half-time, after which The Shaymen failed to muster a spell of pressure, or force home keeper Scott Loach into a save in a poor second-half diaplay.
"We started bright enough. I thought we worked a couple of good moves early doors," said Hughes.
"Then I thought our goal was excellent, a great win-back by Cameron King, we got the ball to Devante, and he did what he does very well. He finished it off very well, a clinical finish.
"At that point, I thought potentially we could go on and get another goal, but that just didn't happen.
"I still thought throughout the first-half we gave a good account of ourselves, and on another day, we might have got another.
"I don't think initially we responded well to the equaliser. We tried to rectify things in the second-half, and we gave away a goal that should have been avoided.
"They broke on us and they scored, from a mistake in midfield. That's what happens because they're a good side, a good footballing team, and they punished.
"Unfortunately, our response to going 2-1 down wasn't what we would have anticipated, and we just couldn't muster up another opportunity.
"Our energy in that second-half dropped, and I t don't think we were active enough against the ball. When we did get on the ball, we gave away easy possession, which you can't do against this team, because they're good on the ball and they keep good possession.
"Having said that, I thought late on, we created the best move of the game and on another day, Devante would have pinched that in-front of the goalkeeper and we'd have gone away 2-2 and been reasonably happy.
"But the first-half we did reasonably well, came in at 1-1 and deserved to be in that position. But second-half I don't think we did enough to get something from the game."
When asked why Town hadn't performed after the interval, Hughes said: "Once they scored the goal, it set a different picture for the rest of the second-half, and I don't think we responded well.
"It came down to quality on the ball, and it just didn't happen for us today."
Salford loanee Rodney now has six goals in 10 games for Town, the latest being a smart low finish from the edge of the box at his old club.
"The boy's done great," Hughes said. "It's been a great signing, but a lot of it's down to him.
"He's been worked with since he got here, and he's listened and learned, and he's taken the chances that have come his way very well.
"He's good around the place, he's a good professional, and he's a good finisher.
"Sometimes the shoe just fits, and the manager's obviously looked at him and thought he could fit in well with how we go about our business.
"He's able to exploit space in behind teams, he's got pace to burn, and he's been very effective."
Hughes confirmed right-back Jacob Hanson's second-half substitution was due to an injury, but he is confident he will be fit for Monday's game with Wrexham.
Youngster Harry Freedman made his Halifax debut as a second-half substitute, something which Hughes said the midfielder has earned.
"He's showed up very well in recent sessions, and he merits his opportunity today," Hughes added.
"He's done very well in most sessions since Christmas.
"He was given the opportunity to come in, in a difficult situation, away at Hartlepool, 2-1 down, but there's a lot more left to see from him."