"We believe these punishments are unnecessarily harsh given the circumstances," the Premier League club said in a statement on their website on Monday.
"We would reiterate that the players and the club are acutely aware of our responsibilities towards setting a good example as role models and upholding the values of the game."
Drogba was banned for six European matches, two of them deferred, for harassing Norwegian referee Tom Henning Ovrebo after the final whistle, screaming insults and launching a foul-mouthed tirade towards a live television camera.
Bosingwa was suspended for four European matches, the last one also deferred for a probationary period of two years, for comments after the match at Stamford Bridge which ended in a 1-1 draw to send Barca through on away goals.
Chelsea have also appealed against the fine of 100,000 euro imposed on them for the conduct of their players and the throwing of missiles by supporters at the end of the game on May 6.
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