Matty Warburton's second-half penalty, his fifth goal in six games, decided a tight contest against The Mariners.
"I thought it was a really professional performance," Wild said.
"Credit to my staff, who have spent hours looking through Grimsby and coming up with a plan to combat them, to beat them.
"I asked them to go away and 'what have we learned?', 'what can we do better?' etc, and they came back with a great plan.
"We had a chance to practice it on Saturday and we've had a chance to implement it tonight.
"When teams high press us we can either shell it or we can be better at playing through the thirds under pressure, and I thought we were better at playing through the thirds under pressure tonight, which really pleases me because they're listening to what I want."
Wild added: "It was a tight game, nip-and-tuck, nothing really in the game, not many chances.
"You're waiting for them to make a mistake and thankfully they did, and we've duly obliged.
"They're a good side, there's some good players, Paul puts together some very good teams, so we knew we'd have to be at our best tonight.
"But I think the team have again showed their professionalism."
When asked if he thought his side had done enough to deserve the win, Wild said: "I thought we played a lot better against them than we did up there, which shows progress.
"Apart from the shot after 30 seconds when they tested Sam, they haven't really tested him. We probably had two or three more shots at goal but we haven't really tested their keeper, so if it had been 0-0 you'd have come away and gone 'fair enough' but it's nice to edge it."
And Wild believes the win is one of the best results of the season so far from his team.
"100 per cent. We've had Southend, Stockport, Grimsby, Wrexham, and we've gone toe-to-toe with them all here, which just shows the character and how good the group's behaving at the moment. Long may that continue," he said.
On match-winner Warburton, the Town boss said: "We always knew Warby would score goals, we brought him here because we knew he'd score goals, he's that number ten that scores goals.
"He scores goals from that position, like he did at Stockport two or three years ago, and he's now bringing goals to his game.
"But don't forget the amount of effort him and Bill (Waters) put in up there, out of possession. He brings a lot to the party and I'm really pleased with him, as I am with all the boys. They're doing well."
Read more from the Town boss in Thursday's Halifax Courier and online later this week.