Ardley’s men found themselves two-nil down after 20 minutes following strikes from Alex Whittle and Akwasi Asante.
But a red card for Curtis Weston for an off-the-ball incident involving visiting player Mark Ellis midway through the first-half changed the game and Solihull secured the three points thanks to goals from James Clarke, Callum Maycock and Harry Boyes.
Ardley said: “It was a disappointing first 20 minutes. I thought we started well for ten minutes, we looked lively and our game plan was working.
"The two times they get into our box we conceded both times and that was disappointing because up until then I had not seen the threat that they carried.
"Obviously the sending off changes the game, we know that. I have looked at it back, it does look like the head (from Weston) goes in. It is from the stand so it is not easy to see but it looked like it and Mark (Ellis) said he definitely got caught on the chin.”
He added: "It is not easy to play against ten-men especially when they are a good team with good players but once we calmed down we started to move the ball well and created chance after chance. When they don’t go in you wonder if it is going to be your day or not we stuck at it and it was thoroughly deserved in the end.
"Credit to them (Chesterfield), they are a good team and they are going to win games.”