Jack Earing's first-half goal was enough to seal the victory for Town and hand them a crucial three points in the race for the play-offs.
"I thought we started really well, on the front foot, pressing them, kept nicking the ball off them, kept going towards goal, got our goal," Wild said.
"They're really good at what they do to try and stretch you, to play through the spaces that you leave, and we thought when we got the goal, we'd drop off them a little bit, let them have the first pass, and I thought until half-time we frustrated them, they never looked like threatening.
"When it's 0-0 they had a really good chance, but once we went 1-0 up and dropped off them a bit to let them have the ball, I'd seen King's Lynn had done that to them on Monday and we thought if we needed to do that, we could do, and I thought it really frustrated them until half-time.
"We knew they'd come out second-half and have a real go, and we just didn't keep hold of the ball well enough second-half.
"They just kept coming back at us. When we did have good passages of play to get in their half, our final ball was rubbish.
"That could have hurt us on another day, but at this time of the year, it's how you grind out three points and we've certainly ground it out today against a really, really good Altrincham side.
"They've caused us problems and I think they're one of the most entertaining teams in the league.
"I'm over the moon to get three points."
Wild admitted his side needed to be better at retaining the ball as Altrincham ramped up the pressure in the second-half.
"We knew we had changes in us, we wanted to try and get Summers and Woodsy on in midfield to get hold of the ball for us, and give us legs and give us energy," he said.
"I thought they both did that, it's just when we got higher up the pitch, we just didn't keep hold of it enough.
"It's a thankless task for Jake up there on his own, we knew that, which is why later on we went to 3-5-2 to try and keep it up there.
"That's something we've got to be better at, but it's the time of the year where you've just got to grind out three points, and however you play, if you come away with three points you've got to be happy."
On match-winner Earing's goal, Wild said: "That's what Jack's good at, that's what Jack's brought to his game this year, driving centrally, which we've been working with him on all season, and striking from the edge of the box.
"Great goal to win a game."
Wild praised the performance of goalkeeper Sam Johnson, who was vital to Town's clean sheet.
"Two really good saves, one in each half," said the Town boss. "You need your goalkeeper every week to pull off certainly one good save and he's pulled off two.
"He deserves that and I'm really pleased for him."
Luke Summerfield made his first appearance in 12 games for Town off the bench.
"Really pleased he's back in the fold, and Woodsy," said Wild.
"We've got really good competition for places, and that can only bode well for the run-in.
"We had planned him being back for Tuesday night but just thought with the week he'd had we could get him on the bench and if we needed him, then we could use him."
When asked if Summerfield could start on Tuesday against former club Wrexham, Wild said: "If we needed him to, yeah.
"I've got some really exciting headaches now ahead of Tuesday."
Loanee Billy Chadwick was not involved again for The Shaymen.
"Bill's still not with us at the moment, hopefully he'll be back next week, but we'll see," Wild said.