Wilson said: "For their second goal the referee got the decision wrong. End of story. Madine got a good header, but prior to the header, Reda Johnson just wiped the keeper out.
"It's a strength of Wednesday to take long throws and play free-kicks into the box and I thought we defended well against those sort of attacks. But on the occasion that you want that little bit of help from the referee, we didn't get it.
"The frustration is that he did see it otherwise he wouldn't have had the whistle in his mouth. When I approached the referee at the end of the game, he couldn't look me in the eye. He just walked off and didn't say a word.
"I can't understand why a 26-year-old is given a Sheffield derby when there are all the Premier League referees out there with great experience. We voiced our concern prior to the game."