The Spireites rued a number of missed chances before falling to defeat after conceding two goals in three minutes from Jordan Slew and Matt Warburton.
"It was a really good performance," Wild told the Halifax Courier.
"I think the game sort of ebbed and flowed, because I thought we started well and then they came into it.
"Then it was them again just coming up to half-time, it just kept bouncing from side to side.
"Arguably when we scored our goal, they were all over us, that was their best spell of the game.
"So it was great to nip their pressure in the bud, I was over the moon, and then to score so quickly after was great.”
He added: "I think the way Chesterfield play allowed us to get some of our strengths out.
"I was dead pleased just how we kept going, our flow, our resilience.
"That's our 18th clean sheet of the season, which shows resilience in the box.
"We're nestled in behind the two biggest spenders in the league's history, I don't think we're doing a bad job.
"Having won today, we're one point off getting the most points this club's ever got, so I think we're doing alright, the lads are doing well.”