Kean watched his Blackburn team block out a late onslaught from Fulham as they held on for a 1-1 draw at Craven Crottage after Ruben Rochina had gave them the lead.
And the Scot, who saw his club pick up their first point of the current Premier League campaign, believes any speculation surrounding his future has no foundation
"I’ve got fantastic backing from the owners," Kean said. "I speak to them most days, and I was [in India] last weekend.
"They’re happy with the way we’re playing, they’re happy with the squad, and I’ve always said that if we can have a good transfer window – which we did, spending sizeable money on the last day, together with the other signings – we’ll have a competitive squad.
“I think we have got at least a squad that is going to finish in the top half.”
As the game neared its conclusion, Rovers midfielder Junior Hoilett suffered a nasty looking injury as he collided with Fulham keeper Mark Schwarzer on the edge of the box.
The Canadian needed over five minutes of treatment and Schwarzer received a yellow card, though Kean had expected the Australian to be dismissed.
He added: "I think it was just the way he spun and fell. He’s got three or four stitches in the side of his head, and he was out for a few minutes. He’s got concussion but he’s back on his feet and he’s in good hands with our medical staff. But it was a nasty challenge.
"I was expecting [referee Howard Webb] to send him [Schwarzer] off.
"I spoke with Howard after the game and he felt that Junior had got the first touch, and there wasn’t any contact before that and [Stephen] Kelly was covering round. You’ve got to respect that decision but at the time and with the pace at which it happened, I thought it was going to be a red card.
He continued: "If Schwarzer hadn’t gone in in that fashion, it would have resulted in a goal, so he’s going all out to get a contact on something, be it the ball or our man.
"As for Junior Hoilett, it’s the last minute for us and a good counter-attack, and he knows that if he can get it flicked over [Schwarzer], then he’s probably going to control it and pass it in.
"I think it’s just a good, professional intent from everybody to go for each ball."