The 40-year-old crowd favourite was unable to command a regular first-team place following the promotion and made his displeasure known with a series of outspoken remarks.
He then ended last season in the reserves after a loan move to Oldham turned sour.
Sport on television Brown said: "I've got no animosity or bad blood towards Dean Windass but I wish it could have ended in a more poignant way.
"My advice to him was always to sit on his last year, and accept the plaudits and credit that he deserved. I dare say fate will dictate that we cross paths again in our careers but we wish him all the best."
Windass' departure does not come as a surprise, and he has this week been linked with a coaching role under new manager Colin Todd at Darlington.
He will be followed out of the Hull exit door by midfielder Ryan France, one of four players to have played in all four professional divisions with the Tigers. France turned down a loan move to Blackpool earlier in the season in order to compete for a place.
Former Sunderland and Leeds striker Michael Bridges is also leaving along with John Welsh, who ended the season on loan at Bury.
Reserve players James Bennett, Joe Lamplough, Matthew Plummer and Tom Woodhead have also been released but Will Atkinson, Steve Gardner and Ryan Kendall are retained.
Youth team products Nathan Hanley and John Leonard have been awarded one-year professional contracts and young player of the year Tom Cairney has signed a two-year contract.