Rovers have zero points from their three Premier League games this season but Kean insists his signings at the end of the transfer window have strengthened the squad to a position where they can finish in the top half of the table.
Kean travelled to India last week to speak to the owners, poultry giants Venky's, but insisted it was a routine visit rather than a crisis meeting.
Asked about the letter from fans, the Rovers boss admitted he shares supporters' frustration.
Kean said: "It doesn't make me feel bad at all, I have a great relationship with the owners.
"I can understand the fans' frustration that we don't have a point on the board right now but I think it's a minority of the fans and we share that frustration that we have not got points.
"I would say bear with us, we said 'judge us at the end of the transfer window'.
"I think we now have a stronger squad than we had last year. If we can start getting points on the board - and quickly - then the top half is certainly achievable.
"One win takes you halfway up the table and we are looking at going down to Fulham on Sunday and being positive like we were against Everton."
Kean said his relationship with Venky's remained "excellent".
"Every time I go there [people suggest] it's a crisis meeting. It just happens to be the same day every month," he added.
"It's not a crisis meeting. They are very happy. I go once a month, we sit down have a lot of conversations and the communication side between myself and the owners is excellent."
New signings Yakubu, Scott Dann, Simon Vukcevic and Jordan Slew are all in the Blackburn squad for their visit to Fulham.
Morten Gamst Pedersen (hamstring) is out however, while David Dunn is doubtful, also with a hamstring problem. Ryan Nelsen will be assessed to see if he has recovered from his knee injury.
Kean spent eight years at Fulham, first in charge of the academy and then as assistant to Chris Coleman and said they were "fantastic" years.
"They have a great chairman [Mohamed Al Fayed] who has a put a lot into the club, I have great memories and I am looking forward to seeing some familiar faces," added Kean.
"Like us, Martin Jol has brought in some new players and they will take some time to settle down but I am sure he will get it right."