Rovers went into the Ewood Park clash on a high after the weekend's shock victory over Manchester United but failed to capitalise on early momentum and were two down at half-time to a brace from Peter Crouch.
They were given hope by a first Barclays Premier League goal for David Goodwillie 21 minutes from time but could not find an equaliser.
The result, which left Blackburn three points adrift of safety, was made all the more disappointing for Kean by defeats for fellow strugglers Wolves and QPR.
The Scot, who felt an early Christopher Samba header should have stood, said: "We feel as though it's a missed opportunity because the way the results have fallen we could have found ourselves out of the bottom three.
"But it's very tight, there's other teams that have been dragged in it now so if we can keep performing and dig another couple of results out we can find ourselves in a much better position."
Kean's job has been made more difficult by the attitude of a large group of fans towards him and owners Venky's but he could have no complaints on Monday as Ewood Park stayed fully behind the hosts.
He said: "I thought the fans were excellent and I'm delighted because it's a young team that we've got, and if they can get that feel-good factor and confidence to get on the ball (then results can improve).
"I think the fans certainly came to the ground positive, even at 2-0 they stayed with us, and it's such a big help. I can only applaud them for that."
Stoke boss Tony Pulis was one of a number of managers to criticise the Blackburn fans for their treatment of Kean, but he was impressed by the atmosphere at Ewood Park.
He said: "I thought the Blackburn supporters were brilliant. They stuck with their team all the way through, and they need to do that."
Pulis also praised Blackburn for the way they pushed his side in the second half, particularly from Morten Gamst Pedersen's set-pieces.
The Welshman added: "I thought first half we played well and played some good stuff. It was a real mixture. You've got to give them credit.
"They've got some great quality from their set-plays and they're a big team. Anything that goes round Samba it's very difficult to win the first ball and they used that very well.
"They kept going for Steve. You didn't see a team out there who had given up hope. If they do that in their remaining games, they'll pick up some points."