Town boss Billy Heath praised the character of his side after they beat 10-man Dagenham and Redbridge 2-1 at The Shay to reach the second round of the FA Cup.
Halifax will now travel to Eastleigh after goals from Tom Denton and substitute Matty Kosylo, the latter coming in the last minute of normal time.
“I thought the players were magnificent, to a man,” Heath said.
“It’s a bit like a mirror image of Saturday, with us missing the penalty we don’t make things easy for ourselves.
“If we score the penalty, and with the boy getting sent-off, the game’s really finished then.
“Once again, it’s another late goal by Matty. But the players were fantastic.
“We lost Jordan Burrow with a bad back, he had a back spasm.
“Then Nathan Hotte has played after spending most of the day being physically sick, but he’s played because we’ve got no other choices defensively.
“And he was magnificent.
“They’ve all put a massive shift in, showed their commitment.
“When they equalised the game shifted, even though they had 10-men.
“Our passing went awry and we looked disjointed and tired.
“But they showed great character and we’ve got another result.”
Town came flying out of the traps and appeared to have two legitimate goals disallowed, one within the first minute from Alex Simmons and another when a Denton header was ruled out for offside.
“I thought the first 25 minutes, half-an-hour, we were absolutely superb and we dominated the game,” said Heath.
“What a finish from Dents. Everyone thinks he doesn’t score with his feet but last season he got 21 goals and nine of those were with his feet.
“It was a wonder strike and he thoroughly deserved it. For the first half-an-hour he was unplayable.
“I’ve yet to see the disallowed goal when we cross it from virtually the byline.
“It might be the right decision but it looked a strange one.
“We should have been two or three to the good.”
Heath didn’t agree with the decision to send off Dagenham’s Ollie Hawkins just after half-time for an alleged push on Simmons.
“I thought it was harsh,” said Heath. “When the boy challenged, it was a coming together.
“They may have got it right but at the time I thought it was a bit harsh.”
On Jordan Sinnott’s missed penalty, Heath said: “I expected Liam (King) to take it but they’re the ones on the pitch.
“Liam missed one on Saturday so Jordan’s taken it.
“It was a good save but being hyper-critical, you shouldn’t miss a penalty.”
Kosylo now has two goals in two substitute appearances, and Heath admits the midfielder is giving him a selection headache ahead of Saturday’s league game at Curzon Ashton.
“He’s banging on the door,” added the Town boss. “He’ll be disappointed if he doesn’t start on Saturday, quite rightly.
“What more can he do? He’s been very direct when he’s come on.
“He takes players on, he’s got great quality and he pops up with goals.”