"Pathological self-congratulation," sniffed Clinton's chief policy adviser and former top State Department aide Jake Sullivan.
The responses reflect the restive mood in American politics and pointed up the social, political and economic currents motivating voters in Britain and the United States.
That mood may be doubly worrisome for Democrats now that Clinton, the establishment candidate, has become the de facto nominee. As in Britain before the Brexit vote, fears about immigration and frustration over government bureaucracy fuelled the rise of outsider candidates in the US.
Several conservative US politicians, meanwhile, cheered the vote. Republican senator Ted Cruz, one of the critics of the president's opposition to Brexit, told supporters on Facebook that Americans needed to heed it. "The results of the #Brexit referendum should serve as a wake-up call for internationalist bureaucrats from Brussels to Washington, D.C. that some free nations still wish to preserve their national sovereignty," Cruz wrote. "The British people have indicated that they will no longer outsource their future to the EU, and prefer to chart their own path forward. The United States can learn from the referendum and attend to the issues of security, immigration and economic autonomy that drove this historic vote."
Alabama Republican senator Jeff Sessions compared the formation of the EU to the Trans-Pacific Partnership, a trade deal opposed by protectionist Republicans and the pro-labour left.
Clinton's new Trump-specific campaign slogan, "stronger together," was the same appeal British Prime Minister David Cameron made to keep Britain in the union, and earlier, to keep Scotland in the UK. Cameron, a longtime politician well known to Clinton, announced his resignation upon the failure of his Remain side.
Clinton appealed for calm after the surprise success of the Leave campaign and said the first priority for the US should be to contain any economic fallout.
Her campaign mocked Trump's promotion of his business in Scotland the morning after the vote. And she tweeted: "Hours after the #BrexitVote, Donald Trump was in the U.K. Talking about how he, personally, would benefit."
Clinton is campaigning against Trump as the voice of experience and reason, while casting him as reckless, ill-informed and bigoted.
Clinton backed Britain remaining in the EU, as did President Barack Obama. "We respect the choice the people of the United Kingdom have made," Clinton said. "Our first task has to be to make sure that the economic uncertainty created by these events does not hurt working families here in America."
Trump's response, Clinton policy adviser Sullivan said, is part of how he responds to crises or events outside his control.
"Rather than consult people who might know something about what's happening, especially given the stakes for American families, he consults only with himself," Sullivan said. "Rather than think about or talk about what's good for the American people, he thinks about and then talks about what's good for himself."
"He said that running a golf course is just like running a country. The American people need a steady hand at the wheel in a time of uncertainty and not a reckless and erratic egomaniac who could drive us off a cliff."