Drogba has apologised for the offence after throwing a coin back into the Burnley supporters and making a rude gesture, but Lampard has called for leniency and wants fans who abuse players to be punished.
"There are two sides to it," Lampard told Metro: "Didier's come out and there's been a reaction, a human reaction I have to say, which Jamie Carragher made once.
"He's come out straight away and said he's made a mistake. People also have got to stop throwing things on the pitch. I was around Didier at the time and I don't know how many coins there were around.
"We've seen referees getting hit, too, so I think people have to take responsibility as a group.
"Didier has to take responsibility as an individual. I hope he doesn't get banned, but it's up to The FA, who are investigating it.
"But if Didier gets banned, are fans going to do this more to provoke people? Who knows? I take quite a lot of corners and it's not unusual to get things thrown at you and lots of abuse, too, and I think it's got to a stage now where it's got to stop."
Former Blues playing legend Gianfranco Zola has also defended the Ivorian, claiming he must have been provoked.
''I know Drogba is a very composed and honest player,'' said Zola. ''He is always fair. If he reacted, maybe he has been insulted and that is not good in football.
''A couple of weeks ago there was an anti-racism campaign. I don't know if this was a racist act or not. The crowd has to respect the players, and the other way round.
''I don't know what happened but I know he is a fair player and an honest player - a straight player. You have to understand they are human beings and when you are playing an important match you are under pressure.
''Sometimes your composure can be lost. It's not easy, you are walking on the edge all the time. A little bit of common sense is good from both sides. There have been a couple of situations when I was struggling on the pitch and getting abuse from the crowd. I was very close to reacting.
''It's totally understandable. Some moments you can hold yourself and others you can lose it a little bit.''