Drogba has apologised for the offence after reacting to some coins being thrown at him by throwing a coin back into the supporters and making a rude gesture.
"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."