Rao admits he is concerned by Rovers' current plight in the Barclays Premier League but is confident Kean is the right man to save them from the drop.
Rovers are just two points above the bottom three after a run of nine games without a win, but Rao told Granada Reports: "If I said I was not concerned, that is wrong, but at the same time I am very positive towards the manager and my players. I have full confidence in them."
He added: "The way they have been playing, there are good times and bad times.
"I think we have to stand behind the manager and the team and they will come out of it."
Kean has won just three of 16 Premier League matches since being appointed after the controversial sacking of Sam Allardyce by the Rovers owners last December.
Rao and his brother Balaji took charge of the club in November when their company, Indian poultry giant Venky's, completed a £23million takeover.
Venky's still have much to do to win over sceptical fans but Rao has asked for patience.
He said: "We are very serious. Each game we are watching very carefully out here. We are committed to each and every fan.
"If you give me some time - one year's time from now - we will surely prove it to you how serious we are. Whatever has to be done for the club and the players, in percentage or money-wise, it will be fulfilled."