"It shouldn't have happened and it won't happen again," Mr Beckett said.
"I can understand why they [complainants] aren't aware of the context of the whole thing. There was no damage done, nothing malicious about it. But it wasn't the smartest thing."
Mr Beckett said the video was organised by an international group which travels and films various activities and publishes their videos for followers on YouTube.
The group, headed by YouTube star Devin Supertramp, had been filming at the Blokart track and planned on filming some sunrise and sunset shots at the Mount, when "one thing led to another" and the video of the group careering through the streets was made.
"It was not what it was played up to be. The tooting and alarms, that's all editing afterwards. There's always going to be haters," Mr Beckett said.
He said that, although he thought the video was blown out of proportion, he respected the police's concern.
"It is irresponsible to some extent but it's all relative."
By 4pm yesterday the video had received more than 906,000 views.
When asked if the video's reach had been worth it, Mr Beckett said "no".
"Out of respect for law enforcement and what they have to do - now they're in the gun as well - I'd have to say no."
Senior Sergeant Ian Campion said in a written statement yesterday the group came to the attention of a police officer when they filmed in January. The group co-operated with the officer, loaded the karts on to a trailer and left.
Now police had see the video, Mr Campion said they were "extremely disappointed with their irresponsible actions".
"In light of the video we are speaking again with riders involved to decide whether any further action needs to be taken."
Mr Campion said police had received no complaints or reports of damage during the filming but asked the owner of the car to contact them if any damage had been received.