Chelsea were incensed by Obi's dismissal in the first half for a challenge on Patrice Evra and contested it, but the FA rejected their appeal and his three-match ban was upheld.
England captain John Terry escaped punishment after appearing to grab Dean's red card.
Chelsea were fined £10,000 in April 2006 for the same charge of failing to control players after referee Mark Halsey was surrounded during a match against West Brom.
They were given a further £10,000 fine and warned as to their future conduct after again being found guilty of failing to control their players during a 1-0 Premiership defeat at Fulham, a charge which the club had denied.
Last season Chelsea were handed a £100,000 fine and reprimanded for their part in a brawl with Arsenal players during the Carling Cup final.