The incident happened when Coulthard apparently failed to keep the flag properly on the front seat of a car designated to take him around the crowd after participating in a race on the Tank Bund here and it slipped out, falling on the ground.
Noting that the flag lay on the ground, a crew member rushed and handed it back to Coulthard, who then sat on the window of the car and started waving it to the crowd as the vehicle moved around after the event.
"I must apologise for dropping the flag...From my point of view we don't have this tradition or rule in our country. So, I would never disrespect the country and I would never disrespect the flag," he said.
"So, I hope you understand that I can only act as to what is normal for me and according to the rules in my country. I am really sorry, I cannot know the rules of every country...So, apologies to your nation. I have tremendous respect for India and respect for the flag and the people," Coulthard, the 13-time Grand Prix winner, told reporters.
Earlier, participating in the Infiniti Red Bull F1 showrun, with the iconic Hussain Sagar as the backdrop, Coulthard enthralled the massive crowd as he reached speeds of more than 280kms per hour.