Kean was the subject of ferocious abuse at Ewood Park before Christmas, when Blackburn lost to Bolton, a result that condemned them to the Barclays Premier League basement.
Since then Rovers have picked up a point at Anfield and now registered the most surprising result of the entire Premier League season so far.
"I hope, in time, the fans who have been negative will turn as well and be with us and make a real intimidating atmosphere at Ewood Park," he said.
"If the players carry on playing without fear, as we did today, we will climb the table.
"I have always respected the fans.
"I have had mail telling me to keep going. Obviously, in the ground and in the local media, it has been negative, which has been disappointing.
"It is a time where we need to get behind what we are trying to do."
That Blackburn achieved Saturday's success at despite the absence of 11 senior players just emphasised the magnitude of their victory.
It also underlined why Kean believes it is imperative for Rovers to act fast in the transfer market in January.
Yet there are fears Venky's will order further sales before they will sanction any purchases, having revealed annual losses in excess of £18million earlier this week.
"I hope not," said Kean.
"It has not been said that is the case. We will try and keep together and bring bodies in.
"We lost key players in the last transfer window. We don't want to do that again.
"We have targets and are moving forward with them. That will be an ongoing process like everyone else. I am sure we will bring people in."