Rovers needed one of their rivals to drop points if they were to clamber their way out of the drop zone on the final day.
Victories for Nottingham Forest and Birmingham meant Rovers' Griffin Park success was insufficient to save them from dropping into the third tier of English football for the first time in 37 years, and becoming the first former Premier League champions ever to do so.
Shearer tweeted: "Devastated for @rovers and for the fans".
The Lancashire club dropped into the third tier for the first time in nearly four decades despite Sunday's 3-1 win at Griffin Park, with Nottingham Forest and Birmingham also victorious.
Blackburn were Premier League champions in 1995, but their fortunes have dived under the ownership of the Indian poultry firm Venky's. "The owners deserve it". "We'll wait and see", he said.
Tony Mowbray is keen to stay at Blackburn and lead a promotion push from Sky Bet League One next season but admits any decision over his future is down to the club's owners.
Che Adams scored the only goal at Ashton Gate and Redknapp, who signed a short-term deal to replace Gianfranco Zola, said: "I don't need to be chasing work". Blackburn were 14th in the top flight back then; now they are heading towards the third tier, a level unknown to them since their return in 1980. "We must play Thursday (against Celta Vigo) and then we go again against Tottenham, but we can not go with everything against Tottenham", the United manager said.
"Paul Senior has today resigned from his role as director of football and operations", said a statement on Blackburn's official website.
But Forest rallied and beat visitors Ipswich Town 3-0, thanks to two goals from Britt Assombalonga and Chris Cohen.
Birmingham won 1-0 at Bristol City to survive, meaning its decision to hire Harry Redknapp with three games left in a last-ditch attempt to stave off relegation paid off.
Jack Grealish's late goal for Aston Villa helped secure a 1-1 draw with Brighton, handing the title to Newcastle United who won 3-0 at home to Barnsley.
Reading, Sheffield Wednesday, Huddersfield and Fulham will contest the playoffs to become the third team promoted.