It is now the fourth highest unbeaten score in the history of test cricket and the 10th highest score in test cricket.
His knock of 335 is officially the second highest ever test score by an Aussie – second only to Matthew Hayden's 380, set in 2003.
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Australia declared at the end of the same over where Warner jumped above Mark Taylor and Sir Donald Bradman's iconic scores of 334.
Warner earlier also broke Bradman's 88-year record for the highest score at the Adelaide Oval.
Scoring at more than five runs an over, Lee told Fox Cricket Warner should have been given a chance by Paine to chase the record, after passing Bradman's mark with more than half an hour of play before the dinner break.
While Mitchell Starc's early dismissal of Imam ul-Haq has eased the pressure on Paine, Lee said Australia should have batted on until the final session of play to force Pakistan to start its innings under the lights.
He also said he didn't agree with Paine's decision on a game-management level, because he says there is not enough rain predicted to fall in Adelaide to put Australia's victory charge in doubt.
"It's not a lot of rain though is it? I'm just thinking, you don't often get that opportunity to go on to get a world record," Lee said.
"Years and years of cricket, and here's a chance to knock over 400 from the great Brian Lara.
"I would have preferred they start the innings under lights with the new pink ball.
"I just think if they went out to Warner and said here's the equation, 'You've got eight or nine overs to bat. If you can pick off another 70-odd runs, good luck'.
"I reckon if there's someone in world cricket that could get 60 odd runs in nine or so overs, it's David Warner."
Aussie legend Shane Warne said he was surprised by the decision, but said he understood Paine's logic.
"I was a bit surprised. Because of the way Warner's batted today I thought he might have gone for the record," Warne said.
"But they wanted to have a crack at Pakistan. They're putting the team ahead of the individual. It would have been nice theatre to see David Warner go for the record."
Mark Waugh also supported the declaration, while England great Michael Vaughan said Paine had "spoiled the party".
Other commentators were much more scathing of Paine.
Warner was also criticised in some corners of cyberspace for scoring the final single that pushed him above Taylor and Bradman's scores of 334.
Warner hit just the eighth Test triple-century by an Australian, waltzing his way to the highest ever Test score at Adelaide Oval. In the most dominant innings of his career, Warner brought up the mark off just 389 balls in the pink-ball Test when he pulled Mohammad Abbas for four.
He is the first Australian to do so since Michael Clarke in 2012 against India, in what was a similarly big first-innings score.
With world-record holder Lara in the crowd watching his score of 400 fall under threat, Warner punished anything too full or too short from the tourists. And there was plenty of wayward deliveries to pick off.
Twenty-two of his 38 boundaries came through either the covers or point, before he began to sweep with confidence off Yasir Shah on the second afternoon. He added 95 to his overnight score of 166 in the first session on day two alone, before racing to the 300-mark halfway through the middle session.
He reacted by sprinting down the wicket and letting off two trademark leaps, before a long look to the sky on what would have been Phillip Hughes' 31st birthday.
His score overtook Don Bradman's 299no as the highest score at the ground, and he has also surpassed Azhar Ali's record for the biggest score in a pink-ball Test.
In doing so, he became just the third Australian in history — behind Clarke and Bradman — to have two Test scores above 250.
