The frank statement, during a tense press conference featuring both drivers, did little to appease the emotional Webber, who led into the closing stages and had been told by his team that he could cruise to victory with Vettel second.
Instead, Vettel ignored team orders and plunged past his team-mate with a risky overtaking manoeuvre, snatching his 27th grand prix and denying Webber his 10th.
"I cannot say much more than I did a mistake, I'm not proud I did it. If I had the chance to do it again I would do it differently," Vettel said.
He added: "When I came back I saw the team's reaction and I had a short word with Mark, it hit me quite hard that, language, I f***ed up."
However Vettel, Formula One's youngest ever three-time world champion at 25, stopped short of pledging that he would make amends by handing a victory to Webber if given the chance.
For Webber, who has played second fiddle to Vettel as the 25-year-old German won the last three world championships, his team-mate's behaviour was galling after orders were issued over the team radio.
"The team rang up and said the pressure is off now, you need to look after the tyres until the end, basically don't fight each other. I turned the engine down... Emotions obviously are probably not the best at the moment," said Webber.
Formula One teams often issue orders to their drivers to desist from competing with each other in order to avoid mishaps once both teammates are well placed.
Webber added that the situation could now prove difficult for the team in the future with trust now shot to bits between the two drivers.
"I'm a huge sports fan. I think we want to see people give their best until the end. It's extremely unusual to have both cars at the end of a race together," Webber said.
"Obviously now is a difficult situation for the future but it's part of Formula One." He added: "We are professionals and we did the job today. But it's not an easy situation for the team and it's always spoken about, always has been and always will be."
Mercedes' Lewis Hamilton, who finished third, was also contrite after team principal Ross Brawn told a frustrated Nico Rosberg not to overtake his illustrious new stablemate in the closing stages.
"I don't feel spectacular to be here. I think Nico deserved to be where I am now," Hamilton said. "But obviously the team thought that with the position of the championship perhaps it was logical to stay in the positions we were in.
"But I have to say congratulations to Nico because he drove a much smarter, much more controlled race than I did today."
Vettel now heads the Formula One championship after the first two races, with Webber third, as he bids to become the youngest driver to win four world titles in a row.