The Springboks claimed the Webb Ellis Trophy for the second time thanks to four Percy Montgomery penalties, a three-pointer from Francois Steyn and an amazing defensive effort in the 15-6 triumph at the Stade de France.
White's side repeated the exploits of the country's class of 1995, and he admitted he was taken aback by the achievement.
"It's an unbelievable experience. It hasn't sunk in yet," he said. "To see the president of our country (Thabo Mbeki) sitting on the players' shoulders holding the World Cup, it doesn't get much better than that.
"It's a massive thing for our country, it doesn't get bigger than that in the context of where we come from."
England had the better of territory and possession, but South Africa scored the points when it mattered.
Steyn's 62nd-minute penalty gave the Springboks a nine-point cushion and they relied on their obdurate defence to see them home.
"I always said defences win World Cups," added White. "It's amazing how history repeats itself. There were no tries in 1995, two tries in the 2003 final and no tries tonight.
"It just shows important defence is. All credit to my Springboks.
"We were defending so well and we never really felt that they were asking questions of our line.
"When we were two scores ahead and we turned their line-out over, we knew they would have to chase it. We slowed the game down and we have learned that over the past four years."
White paid tribute to a valiant effort by England, who failed in their bid to keep hold of their crown.
"I think it would be wrong not to compliment England," he added. "People wrote them off. People talk about pride, passion and teamwork, and they have proved they will not go out without a fight.
"They gave everything they had, but winning back-to-back World Cups is always difficult."
Captain John Smit poured lavish praise on full-back Montgomery, who was flawless with the boot in kicking four from four.
He also showed a superb positional sense and played the last section of the match injured after being shoved into an off-field camera by England replacement Toby Flood.
"Percy deserves the most accolades out of the group," said Smit. "He is the most-capped player in the history of South African rugby and he has copped a lot of criticism.
"But he is the perfect example of a professional. You can't fault him for the fact that he is brave, he took high balls, kicked the penalties right over and shoulder-charged a camera.
"It must be horrible for the people who have ridiculed him for his looks, his hair and his highlights - they must be disappointed he has won the World Cup for us."