Drogba and Bosingwa banned by UEFA
His team mate Jose Bosingwa was also suspended for four UEFA matches for his comments after the second leg at Stamford Bridge which ended in a 1-1 draw to send Barca through on away goals.
The final match of Bosingwa's ban is also deferred for a probationary period of two years.
Ivory Coast forward Drogba will miss the first four of Chelsea's six group stage matches in the Champions League next season while Bosingwa will sit out half of them.
Chelsea were fined 100,000 euro for the improper conduct of their players and the throwing of missiles by the Premier League club's supporters at the end of the tie on May 6.
UEFA said on its website that the players and Chelsea had three days to appeal against the decision.
Chelsea were knocked out in dramatic circumstances when Barcelona's Andres Iniesta scored a crucial away goal in stoppage time, leading to a furious reaction from Chelsea players to Norwegian referee Tom Henning Ovrebo who waved away several penalty claims for the home side.
Drogba harangued Ovrebo after the final whistle, screaming insults and then launched a foul-mouthed tirade towards a live television camera. Bosingwa later described the referee as "a thief" when talking to Portuguese television.
Both players later apologised for their reactions with Drogba saying he would accept any punishment.
UEFA spokesman Rob Faulkner said the sanctions were "fairly strict but appropriate".
Talking to BBC Radio Five he said: "We have to set certain standards. We do have a 'Respect' campaign and the Uefa president (Michel Platini) is instrumental behind that.
"The players are key to that, in setting a good example both on and off the pitch. The club obviously has a responsibility for the way their players behave as well.
"All in all, that's the reasoning for the decision."
The London club said on their website that they were still considering their response to the punishments.
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