An independent FA Regulatory Commission has rejected Blues' appeal for wrongful dismissal.
Dean was sent-off by referee Andy Madley in stoppage-time of Blues 4-2 defeat at Cardiff City.
Dean's challenge on Joe Ralls, as the centre-half went to win a header, did not seem malicious.
Blues mounted an appeal, but the red card was not rescinded. The Commission decided it could not be proven that the referee made a 'clear and obvious' error.
The Blues captain now sits out games against Fulham (home, Saturday) and trips to Huddersfield Town (23 November) and Sheffield Wednesday (27 November).
Madley had awarded a Cardiff a controversial 30th minute penalty when Dean was judged to have pulled the shirt of an opponent at a corner.