The club announced Williams had left after 14 years and he becomes the second high-profile departure from Ewood Park since the Venky's takeover following the sacking of Sam Allardyce in December.
In a press conference broadcast on Sky Sports News, Kean said: "He has been here a very long time. He's done a fantastic job over the years, at times tough times financially for the club.
"He's led the club through so it's disappointing that he has decided to stand down. I've always had a great relationship with John, probably more when I was first-team coach I had more contact with him.
"I've not really had as much contact in the last couple of months as I did in my other job. I wish him all the best and I'm sure he would wish us all the best."