Rovers lost 1-0 at home to Wigan Athletic to seal their fate on Monday, while Wigan ensured their survival in the top flight with victory.
Latics defender Antolin Alcaraz scored with a header three minutes from time to end Blackburn's 11-year stay in the Premier League after a dismal season in which they have won just eight of their 37 league matches under Kean.
Kean said: "It is difficult to put into words what the atmosphere is like in the dressing room.
"A few things were thrown our way in the media last week, questioning our attitude, but I felt tonight we gave it a real good go.
"The disappointing thing is we couldn't take it to the last game.
"I will sit down with the owners and discuss a plan on how to assemble a squad to help us bounce back up straight away.
"We need to try to keep the majority of the squad together and add one or two experienced players that can help us, so from the first game of the season we are ready to bounce back and make sure we are in the division we should be in.
"I have spoken with the owners, like I do every day. We haven't mentioned what has happened tonight, but I am confident we will have a sit down and have a plan in place as quickly as possible."
Rovers, champions in 1995, joined Wolverhampton Wanderers in dropping to the Championship as Wigan climbed to 15th in the standings, securing their top-flight status with one game left following a superb late run including wins over champions Manchester United and Arsenal.
"It doesn't seem real yet," Wigan manager Roberto Martinez said. "It's a great feeling because you could feel the tension and it was a cagey affair.
"To do that and to keep a clean sheet - to have that and what it means is incredible. Eight years in the Premier League
"It's been a great run but football is about the players. It's very easy to say the right things but what matters is when you cross the white line to be brave and arrogant.
"All I do is allow them to enjoy their football and the credit goes to the players.
"You get really high pressure. We've been in the bottom three for a long time. They made the football club proud and the chairman proud."
Bolton Wanderers or Queens Park Rangers will join Wolves and Blackburn in the championship next season.
Bolton, two points behind QPR, must beat Stoke City on Sunday to have any chance of survival and Rangers need a point at Premier League leaders Manchester City to guarantee staying up.