Khun Top went on to say “necessary decisions” will be made to “rebuild, improve and restore the standards expected” at Leicester.
Manager Rowett, who succeeded Marti Cifuentes in February, had 14 games to save the club from the drop. They were relegated after 12.
Leicester had already been docked six points for historical spending breaches when Rowett took the job, but the 52-year-old told BBC Radio Leicester he “will be the first to hold myself accountable” for the part he played in the relegation.
But Rowett is just one of six permanent bosses to have been involved in the club’s three recent relegations.
It started with FA Cup-winning manager Brendan Rodgers, who was replaced by Dean Smith in 2022-23, while Steve Cooper was succeeded by Ruud van Nistelrooy last term.
Enzo Maresca, the only manager to see out an entire campaign in the past four seasons, oversaw 31 wins when he guided Leicester to the Championship title two years ago.
Since then, Leicester have won just 17 of 82 league matches to suffer back-to-back relegations.
Rowett is contracted until the end of the season and was evasive about his future, saying only that “anyone would like the challenge and like to rebuild” Leicester.
He did add that the club’s hierarchy “need to act decisively” after relegation.
“In order to bounce back quickly, of course any club in this position, you have to learn the lessons and make sure those things don’t happen again,” said Rowett.
“I’m not saying I’ve had assurances at all – that is not my remit. It’s for the club to decide on what they do, and this is my opinion of how decisive you might need to be before the start of next season to make sure you hit the ground running.”
