The 30-year-old was released by the Tigers at the end of the season after they failed to pull off an escape on the final day and finished three points adrift of Aston Villa, who ended up in 17th.
Reflecting on relegation, Rosenior said: “It’s devastating – not only for the club but for the surrounding area as well.
“It’s a very hard working community here and to have a Premier League team brings with it fantastic economic investment and also it gives people something to dream about.
“For us to have failed in staying up, I’m personally devastated and I know everyone connected with the club is as well.”
Although he is disappointed to have been let go after five years at the KC Stadium, Rosenior is sure that the club retain the management and playing personnel required to make a swift return to the top flight.
He added: “The manager’s got fantastic experience. He’s already won promotion at this football club. I think we’ve got some of the most talented young players in the country – the likes of Andrew Robertson and Robbie Brady. There are also some experienced players that have been and done it – the likes of Michael Dawson and Tom Huddlestone.
“The list goes on. So, if they can get together and have a good mentality next season, I’d be delighted to see them get promoted again.”
On his own future, Rosenior said: “I’d really consider retiring as a player and moving into management. I love playing football, it’s my passion to play but wherever I go next I want to build the blocks to become a coach and a manager.
“So if a good opportunity came up to build a team, build a club and build a philosophy of a way of playing, I’d seriously consider it.”