The striker confronted referee Tom Henning Ovrebo after the match and launched a foul-mouthed rant in front of TV cameras.
The striker said he "overreacted" and was sorry for setting a bad example to "those watching at home, especially children".
In a statement on the club's official website he said: "'I was very upset at what happened during the game, but having seen the pictures on TV I accept that I overreacted.
"'I also fully accept that the language I used did not set a good example for those watching at home, especially children. I regret that in the heat of the moment I let out my incredible frustration and disappointment in this way, and for that I apologise."
A Chelsea statement also posted on their website this evening put Drogba's erratic behaviour down to "high emotions and frustrations".
It read "While it is clear that some of the events last night were regrettable,
they occurred only because of the high emotions and frustrations which
arose from the disappointment of a controversial defeat in such an
important game.
"Chelsea welcomes Didier's statement today which was made honestly and after reflection. We are all acutely aware of the responsibilities that lie with both the club and its players towards setting a good example as role models.
The club added that it was awaiting UEFA's comments following a review of the match officials' report.
Drogba, who had been substituted in the second half, was shown a yellow
card for coming onto the pitch to vent his fury at Ovrebo after the
final whistle.
He was incensed at the referee’s refusal to award Chelsea two
spot-kicks in the first half at Stamford Bridge when he and Florent
Malouda were brought down.
The Norwegian official also rejected two handball penalty appeals after the break when Gerard Pique handled as Nicolas Anelka tried to go past him and in the final seconds when Michael Ballack’s shot hit Samuel Eto’o’s arm.
That last claim came after Andres Iniesta had lashed home a 93rd-minute leveller for Barcelona to cancel out Michael Essien’s opener and put the Catalansahead on away goals.
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