Town boss Billy Heath felt his side did enough to win after they were held to a 0-0 draw at home by Stockport County.
Halifax are now seventh in the National League North after the draw, in which they kept their first clean sheet in 14 games.
After a below-par first-half, Town were much improved after the interval, and went close twice late on through Matty Kosylo and Liam King.
Heath said: “I think we deserved three points.
“They might say different. It was a competitive first-half but second-half we definitely deserved to win the game.
“We’ve got three wins and a draw in the last four fixtures and we’d have been pleased with that before those games.
“We played some good football, I’m just disappointed we didn’t get three points.”
Heath felt his team were much better after the interval.
“I think they edged it in the first-half,” he said. “It was scrappy, both sets of players knew what was at stake.
“We weren’t as good on the ball as we wanted to be.
“But in the second-half there was only really one team in it - Stockport haven’t had a shot on goal in the second-half.
“Unfortunately we couldn’t take our chances - we created some good opportunities.”
On Kosylo’s chance, the Town boss said: “Adam Morgan has done ever so well, he’s drawn the lad in and played a great ball, the weight of the pass was fantastic.
“Matty’s had a decent first touch and I don’t think anyone in the stadium could believe it when it went past the far post but that’s what happens sometimes.”
And on King’s effort that was cleared off the line, Heath said: “He did ever so well. We were slightly concerned before the game how he would last but he’s got a good engine, he’s fully fit now.
“It was a golden chance, he’s created it himself, he’s gone round the keeper.
“In his position he can’t do any more, he’s got a great contact on it and the lad’s come round and covered his keeper.”
Heath also praised the impact of substitute Tom Denton, adding: “He gave us more of a target. He probably won 95 per cent of the aerial balls.
“When he’s up there we sometimes get a bit lazy and go back-to-front too quickly because it’s an easy ball.
“We spoke about it in the week that we just wanted to keep playing and passing the ball when he did come on.
“I thought we mixed it up really well and sometimes we didn’t put it in that area enough for him.
“We had a couple of opportunities when we got behind them and we were looking to slot it along the ground when you just need to stand it up for him.
“But he’s done well, but so did Richard Peniket, worked tremendously hard but it just didn’t fall for him.”