"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," Ferguson said in a statement on the Manchester United website (www.manutd.com) on Saturday.
"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."
In comments made after the Premier League game on October 3. Ferguson had strongly criticised Wiley's fitness levels.
Ferguson said in his statement on Saturday that he had never wished to imply that Wiley was a bad referee or that his performance in that game had been poor.
"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," Ferguson said.
Images: Manchester United vs Arsenal
Manchester United win English Premier League
Wanna have lunch with Sir Alex?
Manchester United whip Chelsea
One more time, Oprah!