Kean announced on Friday that he has been "forced" to step down from his post after his position at Ewood Park became "untenable".
"Steve has, after a great deal of thought, resigned," said Shaw. "It was completely unexpected.
"He travelled down with the team ahead of our game at Charlton tomorrow, but he must have been giving it an awful lot of thought owing to the pressure he's been under.
"With the things that have gone on, over weeks and months, he's decided it's in the best interests of himself and the club that it's time to move on.
"I have spoken with spoken with [Rovers owner] Anuradha Desai and she is very disappointed as she was close with Steve. Owing to time differences, I don't have anything else."
Rovers are at Charlton Athletic in the Championship on Saturday.