The FA asked Fergie to explain his comments and he has issued a public apology to Wiley.
"I apologise to Mr Wiley for any personal embarrassment that my remarks may have caused and to the FA for going public with my views," he has said on the club's official website.
"In retrospect, I accept that this could be deemed as expressing those views in an inappropriate forum.
"It was never my intention to bring the focus of intense media attention on Mr Wiley. I intend to contact him personally after I return from a trip overseas during this international break.
"I would wish it to be noted that I have always respected Mr Wiley's integrity and that I did not state or imply:
1. That Mr Wiley is a bad referee;
2. That he was in any way biased;
3. That decision-making generally during the game was poor, or
4. That he missed any key incident during the game.
"My only intention in speaking publicly, was to highlight what I believe to be a serious and important issue in the game, namely that the fitness levels of referees must match the ever increasing demands of the modern game, which I hope will now be properly addressed through the appropriate formal channels."