Second-half goals from top-scorer Billy Waters, who started on the bench, saw Halifax return to winning ways following back-to-back defeats.
"I thought we were back to us today - aggressive to win the ball back, tactically astute in terms of the plan," Wild said.
"We've watched them, and teams that go up against them try and bop it through them so we wanted to be the team that let them have the first one and when it came into our block, we can nick it off them, and I thought we got it bang on.
"So dead pleased tactically. I thought we got back to us.
"First-half we've hit the post and had one cleared off the line, and the keeper's made a great save from one.
"We worked chances all game, it was just about being patient and knowing the openings would come."
When asked what he felt was different from Halifax's out-of-sorts display in defeat at King's Lynn last week, Wild said: "Our attitude and our application, our attitude towards the game was front-footed, and our application of the tactical requirements was bang on."
On what he said to his team at half-time, with the game still goalless, Wild said: "Play with more tempo when we got in their half and squeeze them in their half more.
"We went side-to-side a bit to try and find the openings but when we went side-to-side we weren't stepping in with it and squeezing them, but we did that better second-half.
"And then to be patient when we had them low. Our chances first-half came from being patient when we had them low, and our worst chances came from when we tried to force it."
Waters played the full 90 minutes for England C in midweek in their 4-0 defeat to Wales.
Explaining why he was only on the bench, Wild said: "I thought Billy looked tired last week at King's Lynn. He's put so much effort into this season, I thought he looked tired.
"And then he's been away with England and let's have it right, they got the runaround on Wednesday night, and I just felt like I needed to, one, freshen my team up, and two, give him a break.
"Some would say I've been vindicated in what I've done."
Wild added: "I said to him when he left my office on Friday, although he was completely fuming with me, I said 'leave here with a positive, and that is instead of grafting for other people to get the chances late in games, you're going to come on fresh and get your own chances because you'll be fresh'.
"I think we've got it right and I'm pleased we've got it right because if we hadn't I've had got lambasted."
Midfielder Kieran Green made his first start since January for The Shaymen.
"He covers the ground doesn't he, he just gives us that protection," Wild said.
"I think the centre-haves like him playing because he gives them that layer of protection as well.
"Don't get me wrong, I don't think he's as sharp as he can be at the moment but I thought he gave us a guile in the centre of midfield that we haven't had in recent games."
Wild said Green wasn't taken off with an injury, adding: "It was always my plan to take him off.
"We were umming and ahing ten minutes before we did it, but when we did it, it was the right time."