Winterbottom acknowledged the rule was in place for safety reasons but felt he was not doing anything unsafe. He believed the rule was inconsistent as he was allowed to do a burnout after winning Bathurst in 2013.
"The crowd loved it and I could hear them cheering on and if the Ford fans love it, in the stand, it's worth every cent," Winterbottom said on Inside Supercars of his Sandown celebration.
"They say safety and stuff ... [but] I'm almost on the horseracing track [inside the circuit] I'm that far to the left and the grandstand is located right there.
"To be honest, the fans went up - they were erupting and they were loving it, so I think it kind of hit me there.
"Anyway, $3000 for a burnout, you cop it. They [CAMS Stewards] will have a good couple of bottles of wine over Christmas - that's where the money tends to go, the Christmas fund.
"But it was worth every cent, to be honest. My wife [Renee] doesn't think that, but worth every cent - a bit of a joke, really."
Winterbottom said he learned about the fine after Renee saw a news article on Facebook. However teams are notified and must sign off on all penalties before the official Stewards report is made public.
"It was a bit of a shock - a $3000 Facebook update that Renee read [on] Sunday night," he said.
"Then Monday morning Cassandra from CAMS sends you this beautiful email saying, 'well done on the weekend, FYI $3000 invoice attached'.
"But anyway, the fans loved it, it's an entertainment sport so if they want to kill the entertainment that's up to them."
Winterbottom has already dealt with the fine: "I think the cash has been paid because if you don't pay in 24 hours or whatever it is they suspend your licence".
"I'm glad it was a good burnout because if it was a bad one I would've been even more upset - but it was a good burnout," he added.
While the burnouts mostly go smoothly and excite the crowds, there have been some embarrassing moments - Will Davison tapped the fence and dented his car at Townsville in 2013, and Jamie Whincup speared off-track into the dirt at Tasmania in 2008.