Drogba could be sanctioned by UEFA for confronting referee Tom Henning Ovrebo and launching a foul-mouthed rant in front of TV cameras following the midweek draw with Barcelona.
Hiddink admits Lampard's response to Chelsea's European demise was far more balanced as he congratulated the Catalan team and swapped shirts with Andres Iniesta.
''Frank also felt this injustice but you could not change what happened at the end,'' he said. ''Instead, calm down and congratulate the opponents. Didier can learn something. He overreacted.
''In the heat of the game I understand reactions. But it must slow down after seconds or minutes. You can fight and defend and have your emotions, but there must always be a level of dignity.
''Didier is extrovert in showing his fire. He knows now also - otherwise he wouldn't have apologised - to use it when it should be used.''
Hiddink will give careful consideration to whether to start Drogba in the Premier League clash with Arsenal.
Drogba limped off in the 72nd minute with an ankle injury and Hiddink must decide if he fit enough in body and mind to face the Gunners.
''I have a few hours to think about that. It's important to ease down a bit now and get the emotions in the normal 'concept', then we'll see,'' he said. ''Didier had some physical problems in his ankle. We'll see, physically and mentally, if he can play.
''I have to reflect very calmly before taking a decision on this.''
Chelsea sit third in the Premier League with the FA Cup their last remaining chance of winning any silverware.
Hiddink has won plaudits for his work at Stamford Bridge since replacing Luiz Felipe Scolari and he wants to leave his mark on the trophy cabinet before he departs in the summer.
''I was already determined to win the FA Cup but hopefully we'll achieve our first aim set in February and that's to qualify for the Champions League again,'' he said. ''When things are going well you can't just be satisfied with that as a target at a big club so we extended our targets.
''In February people would have raised their eyebrows if we said we'd get to a final. But, being there, we're very determined to win. I want to leave having won something.''