Speaking at a meeting organised by the Blackburn Rovers Action Group on Saturday, Singh stated under-fire manager Kean would be dismissed if he lost three consecutive npower Championship games early in the season and likened long-serving wideman Pedersen to a "pensioner".
He told the Lancashire Telegraph: "I would like to extend an apology to Steve Kean because some things were said on Saturday. I think they would have hurt Steve Kean's feelings and, for that, I sincerely apologise.
"Some things are said in jest that don't come across like that when repeated, but I am not making excuses.
"I apologise for hurting any feelings. I would also like to apologise to Morten Gamst Pedersen for what was said. There are no excuses and Morten is a great character.
"My blunt honesty also sometimes upsets people and sometimes rubs people up the wrong way. I am making efforts to bring the club back to the fans and, in trying to do that, I have gone too far. I am trying to find the middle ground."
Former Malaysia defender and television pundit Singh was appointed at Ewood Park this summer to mediate between Kean and controversial owners Venky's, while also attempting to mend severely fractured relations with some sections of the club's support.