"It's just awesome to get that accolade but we're pushing hard here. Struggling a bit at the moment but that's alright.
At the end of the video, posted by Team Brunel, Oracle Team USA's wing trimmer Kyle Langford, who lost the America's Cup to Burling and Team New Zealand, said he was thrilled for his teammate in a tongue and cheek manner.
Langford later paid tribute to Burling alongside several of his teammates in a separate video posted on the team's social media channels.
"To win world sailor of the year two times obviously shows he's a pretty good sailor, up against the best of the best, and to win it in different disciplines - the America's Cup and the Olympics is seriously impressive," said Langford.
Navigator Andrew Cape said having Burling on board was "like having Mick Jagger in your garage band".
Team Brunel are currently fifth in the second leg of the Volvo Ocean Race from Lisbon to Cape Town.
Burling beat out Thomas Coville, Armel Le Cleac'h and Team New Zealand teammate, Australian skipper Glenn Ashby, for the award.
Dutch sailor Marit Bouwmeester took out the women's award.