Webber and the team announced the decision on Saturday, the date of the Australian's 35th birthday, ending months of speculation.
It had been suggested that, after five years with the team, Webber would call it a day. But he now insists that was not an option.
"We announced over the weekend I am going to stay with Red Bull in 2012," said Webber in his BBC Sport column.
"It might look as if it took a long time to sort out, and I was weighing up various possibilities, but in the end the contract talks were done very quickly.
"I've been an integral part of Red Bull since the start and I still enjoy it there. It would have been a mistake to stop racing."
Webber claims he is "still driving well", and although 92 points adrift of team-mate Sebastian Vettel in the drivers' standings, is adamant he can still win this year's title.
"I had a bit of a slow start to this year because it took me a little while to get on top of the new (Pirelli) tyres," added Webber.
"I'm looking forward to taking on Seb - and everyone else - again next year, but this year isn't over yet.
"There are still seven races to go, starting with Monza (Italian Grand Prix) next weekend, and anything can still happen."