Rodgers, 36, was sacked at a board meeting late on Wednesday afternoon after just 195 days in the job.
But Madejski insisted the team's poor start to the season gave them no choice.
First team coach Dean Austin and football consultant Frank Lampard snr have also left the club.
And in new twist, Madejski confirmed that temporary manager Brian McDermott could now land the role on a permanent basis, shattering rumours that Steve Coppell may return or that Darren Ferguson, Gareth Southgate and Alan Curbishley are the leading contenders.
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