Brown signed the former Cheltenham man in the summer as a replacement for retiring club captain Ray Warburton but an injury-ravaged season has seen Brough struggle to make an impression in his 20 first team starts.
Manager and player met up on Friday where it was mutually agreed that Brough would leave once it became clear he could not fulfil the terms of his contract in order to re-sign.
The clause read that Brough had to complete 32 games in his first season in order to guarantee himself a new deal.
Brown said: "John's a fantastic, honest pro who's had a catalogue of injuries and has been chasing his own tail for most of the year.
"A fit John Brough would have been a fantastic to us this year, you can see that we've struggled in that department.
"He's never been able to get himself fit enough to enjoy his game. I respect the fact he said that it hasn't really worked and the fact he's looking to get a game somewhere else.
"If anybody you blame the manager if the player gives his best and if it doesn't work out then so be it. I wish John all the very best."
In Brough's absence, Brown has now laid down the gauntlet to transfer-listed Tobi Jinadu to cement a regular starting place after an encouraging performance on Saturday.
With thanks to the Aldershot News.