Kean walked away from his post at Ewood Park after 21 months on Friday, claiming in a statement that he had been "forced" out as his position had become "untenable".
The decision came at the end of a week which has seen more intense speculation that the axe was set to fall on the 44-year-old Scot, who has been a much-derided figure throughout his time in charge of the club.
He oversaw their relegation to the npower Championship in May, which only inflamed the tensions between manager and supporters.
Despite terrace unrest, though, the Venky's remained faithfully loyal to Kean, giving him two contract extensions after handing him Sam Allardyce's job, as well as backing him heavily in the transfer market.
The news of his resignation came as a surprise to all at the club, with Shaw initially saying: "I have been travelling down to London and this is the first I have heard of it."
But when later contacted, he said: "Steve has, after a great deal of thought, resigned. 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 Anuradha Desai (the club owner) and she is very disappointed as she was close with Steve. Owing to time differences, I don't have anything else."
On Kean's claim that he was forced to stand down, Shaw added: "I can't comment on that. He's decided tonight to call it a day, and the thoughts on why are with Steve.
"As everybody knows, every day of the week we're waking up to a fresh Steve Kean story. I think he has done remarkably well to keep plugging away under the pressure he has been under."
Kean, whose assistant Eric Black will take the team at Charlton, caught his club on the hop when he released a statement through his lawyers at 7pm this evening.
At a time when Rovers' official website was carrying a story of the former Fulham assistant boss talking of a positive week, he said: "For reasons that I cannot discuss on legal advice, it is with deep regret, given my hard work and service for the club for a number of years, that I have been forced to resign as manager of Blackburn Rovers Football Club with immediate effect, due to my position as team manager becoming untenable.
"I wish to thank all the players and coaching staff for their great support and the majority of the fans, who now see their club heading towards an automatic promotion position back to the Premiership. I wish the club all the very best for the future."
While there was no further comment from Kean, Black or the club's operations manager, Paul Agnew, members of the club's support were delighted.
Claiming "liberation", the Blackburn Rovers Action Group were quick to respond to the news, with secretary Mark Fish saying: "I am delighted. It's been a long 12 months for all involved, and I never thought I'd see the day when he went.
"The supporters are liberated and free of Steve Kean. I am just enjoying the fact that he has gone.
"He has treated the supporters with contempt. We've got 8,000, 9,000 boycotting and empty seats are one thing he can't mask.
"I have longed for this."
The action group, who have regularly protested against Kean's employment throughout his reign, issued a more formal statement in which they said: "Today will go down as the day when Blackburn Rovers was liberated from the man who has brought a whole club's supporter base to their knees with tears.
"They have had thoughts of helplessness and pure anguish at what they have seen unfold at Blackburn Rovers since that ill-fated day he was appointed in December 2010.
"Never in the club's history has one man brought so much despair to the terraces and survived against all odds like Steve Kean has managed to - until today."
Having gone through last season with little dissent from his boardroom, Kean found newly-installed director of football Shebby Singh a different beast over the summer.
He initially told Kean he would be sacked if he lost three games in a row, while earlier this week said the situation was getting "worse by the day".
The Action Group now want to build bridges with Singh and the Venky's, though, saying: "Now is the time for all supporters to unite, put their full support behind the manager's replacement and the players and be the club's 12th man in the quest for promotion."
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