Two goals from Billy Waters and one from Matty Warburton saw The Shaymen get back to winning ways with an impressive performance against one of their promotion rivals.
"I was really impressed with how the players implemented the game-plan," Wild said.
"I thought you saw two sides of Halifax today. I think you saw first-half how good we are as a football team and how we can hurt teams football-wise, and second-half, they were by far the better team second-half and we had to be resilient, defend our own box well.
"They had 17 corners, and they're obviously going to get a chance at some point, but we showed a real resilience in the second-half and I'm dead proud of them today."
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Town's performance showed a massive improvement from their previous two league games, where they lost 1-0 to Maidenhead and Boreham Wood.
"There's going to be bumps in the road across the season, there's going to be defeats and things that don't go our way, that's just football," said Wild.
"But one thing I'll say about them is they performed in training like they performed today, so it was a matter of time before we got back to where we needed to be.
The Shaymen took control of the contest in a dominant first-half, and led 2-0 at the break.
"We'd looked at why did we beat them at home, we looked at the fact that Dagenham are a really good football team, so you've got to stop them playing forward, you've got to starve them of the ball, you've got to be in contact all the time," Wild said.
"We watched Stockport's game against them last week and that was very similar, Stockport got their distances right, got in their faces, stopped them playing, and I thought 'that's what we've got to do'.
"I was showing them clips in the hotel last night 'that's how we have to play' and to a man, subs included, they've gone and implemented the game-plan, so they deserve immense credit. As a group of lads, fantastic today."
And Town defended well in the second-half to withstand a barrage of pressure from the hosts.
"Getting pressure on the ball, bodies on the line, no-one can say that this group don't care," Wild said.
"This group care, this group have got a willingness, a drive, a want to be better and I thought you saw that in abundance today."
On Waters, who netted his first goals in 10 games, Wild said: "I could have done with him not doing that for another two days until the window shuts!
"I said to him in training on Thursday when I told him he was playing off the left that I fancied him for a goal.
"I think him playing off the sides gives him a bit more space, a bit more freedom, you're not doing the fighting work that I thought Aaron (Martin) did phenomenally well today.
"He deserves those goals today."
Town also looked more comfortable in their more familiar 4-2-3-1 system.
"Personnel-wise I had to play 3-5-2 on Tuesday, I didn't have much option," Wild said.
"But it was back to what we are today, back to who we ae today and it paid dividends."
Captain Niall Maher missed the game through injury.
"He's rolled his ankle, a bit like Greeny. They're the ones you can't do anything about," Wild said.
"We're hopeful he'll be back in training late next week."
Midfielder Kian Spence also missed out with a hamstring problem.
"Kian has been out running over the weekend and getting up to pace, so we're hopeful he'll be in contention for next weekend as well," Wild said.
The Town boss said Jordan Slew will be back in training on Monday as his illness has now cleared up.
On striker Matty Stenson, Wild said: "We had him scanned again the other day, just to make sure there was nothing in there, so he'll now bump up trying to get back in the team.
"When you've been out for so long, you feel every knock, bump and movement, so it's important we got it right, got him scanned."
And on midfielder Kieran Green, the Town boss said: "We're still waiting for the swelling to come out. We're still probably be thinking three to six weeks until two weeks in, until the boot's been on for a couple of weeks, until we know where we're at with it.
"Then we'll decide whether it's three, and it's healing really well, or a few more weeks."
Asked about speculation linking Town to former Oldham forward Zak Dearnley, Wild said: "I've heard we've been linked but we'll see what happens."
And on further additions to his squad generally, Wild said: "After today I'm not sure!
"That's thrown me, but that's what I want, I want people to come in and go 'play me'.
"And a lot of players have done that for me, so that's great because it shows people are up for the fight and we've got a squad here that can compete and fight."