Venky's have made the plea on Rovers' official website as unrest is senced amongst the fans after the side has picked up just one point so far this season. Rovers are now rock bottom and are favourites to suffer the drop at many bookies.
Around a thousand fans are expected to go on a protest march this weekend as they grow frustrated at Kean's management.
The statement read: "We understand that there is a sense of disappointment and anger amongst our fans at the recent performance of our team Blackburn Rovers, which was not up to the expectations of the fans.
"We fully understand your feelings and share your disappointment.
"At times like this, when the team is going through a bad patch, they need all the support and encouragement they can get from the fans to boost their morale and enable them to perform at their best.
"This is the time when the fans can make a difference by lending their full support and to cheer the team more vigorously than ever and help the players to renew the confidence in themselves.
"On behalf of Venky's we would like to reassure the fans that we are fully aware of our responsibilities towards them and the club and to football.
"We are fully committed to making sure that the team's performance improves and that the recent setbacks do not stand in the way of regaining our club's standing in the Premier League and in the admiration of our fans."