Singh told an open forum with the club's supporters at the weekend that Kean will face the sack if he loses three games in a row in the Championship season.
"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."
Blackburn were relegated to the second tier of English football last season.