Singh had suggested that Kean would be sacked if Rovers lost three games in a row next term and labelled the long-serving Norwegian a "pensioner" but has now retracted his claims.
"I would like to extend an apology to Steve Kean because some things were said on Saturday," Singh told the Lancashire Telegraph.
"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."