He said: "I gave her a suggestion and I think she found it too brutal".
One objector said: "Donald Trump has done a lot better than our Governemnet".
"So if they go in a slightly different route [on Brexit] - and I know they do want independence. if they are going to go in a certain route I just said that I hope you are going to be able to trade with the United States".
Grant White, 32, carried a sign depicting Trump as the Twitter bird symbol wearing a swastika around his arm.
Earlier tens of thousands of protesters gathered in central London to denounce the visit for stoking "division along fault lines of fear and hatred".
Following his meeting with Mrs May, Mr Trump described United States and UK relations as "the highest level of special" and insisted the Prime Minister was a tough negotiator. "I just want to party with these people forever".
He suggested this was not what voters wanted, said he had advised May to take another path and added that Boris Johnson, who quit as foreign minister over the plan, would make "a great prime minister".
"We have got to look at a future world which isn't dependent on taking 4% of your money to put into arms", he said, referring to Trump's call for North Atlantic Treaty Organisation allies to double defense spending targets.
"I think it's a travesty of British values".
Asked by a US reporter if he regretted his comments to the Sun, Trump looked away, shook his head and pointed at the reporter. One protest group has been given permission for a balloon in the president's image, shaded in orange and dressed in a diaper, known as the "Trump Baby Blimp", to hover over Parliament Square Garden.
He said May's plans to bind Britain's economy closely to its European partners after Brexit would "probably kill" its hopes of a USA trade deal.
Ms May also thanked the US President for his support over Russia, which Britain has blamed for a nerve agent attack on a former Russian spy in south-west England in March.
For those who hadn't prepared their insults at home, piles of placards emblazoned with anti-Trump messages - such as "Dump Trump" and "World's #1 Racist" - lay banked by Oxford Circus underground station for anyone to pick up.
More protests are planned in Windsor, where the Trumps will meet the queen later, and in Scotland, where the president plans to spend the weekend at one of his golf courses.
But he praised Mrs May as a "very tough negotiator" and described her as an "incredible woman" who is "doing a fantastic job". The newspaper released lengthy clips of the interview that showed Trump saying that May did not take his advice on how to handle Brexit, saying she "wrecked it".
According to the Sun, Trump also went after Khan - London's first Muslim mayor who he has feuded with in the past over a travel ban for people from several predominately Muslim states - saying he has done "a bad job", and was soft on terrorism. It didn't go without notice that, even though it's not mandatory, Trump and the first lady did not bow or curtsy when they greeted the queen.