When Drogba opened the scoring in Wednesday’s Carling Cup clash a coin was thrown on to the pitch and the Ivory Coast international threw the coin back into the Burnley crowd.
“This is something I want to make clear. I tried to celebrate the goal and I received some things at me,” said Drogba, who was shown a yellow card.
“The big mistake I did was to throw it back so if someone was hurt, I just want to apologise for it.
“This is not something I should show in a football match and I want to apologise.
“It was an incident in the heat of the moment and I regret it. It was just a mistake and nothing more.”
The Metropolitan Police will also be investigating the incident at Stamford Bridge.