Clinton said the North Koreans "have now been denounced by everyone".
" They have become further isolated. And it is not in the interests of the people of North Korea for that kind of isolation to continue."
The North, describing the sanctions resolution as a "vile product" of a US-inspired campaign, said it would never abandon nuclear weapons and would treat any attempt to blockade it as an act of war.
"We'll take firm military action if the United States and its allies try to isolate us," an unnamed foreign ministry spokesman was quoted by the state-run KCNA news agency as saying on Saturday.
The statement also warned that the North would "weaponise all plutonium [in its possession]" and had "reprocessed more than one-third of our spent nuclear fuel rods."
The UN resolution, passed on Friday, banned all weapons exports from North Korea and authorised member states to inspect sea, air and land cargo, requiring them to seize and destroy goods that violate the sanctions in response to a nuclear test last month.
It was passed as media reports suggested that North Korea could be planning a third nuclear test.
Alexander Neill, the head of the Asia security programme at the Royal United Services Institute for Defence Studies in the UK, told Al Jazeera that while the warning was largely "bluster", it was also a serious threat.
"This [threat of enrichment] is not a new phenomenon," he said.
"It would take a long time and sophisticated technology to convert plutonium to missile-grade material, but it is a gesture with a lot of teeth behind it.
"When it comes to the international reaction, the only option is for the UN Security Council resolution.
"It is almost certain that the US and Japan will enforce a blockade which will put a pincer movement around any of the sea trade going in and out of North Korea.
"The question is whether it will have any result inside North Korea. The regime has proved resilient to sanctions in the past," he said.
North Korea's nuclear test in May defied a previous Security Council resolution adopted after the North's first underground nuclear test in October 2006.
Zhang Yesui, China's UN ambassador, said the resolution showed the "firm opposition" of the international community to North Korea's nuclear ambitions.
The backing of China, one of North Korea's key trading partners and regional allies, and Russia for the resolution gave greater weight to the new sanctions as they have been reluctant to act in the past.
"To a certain extent, China has been happy to leave North Korea to its own devices," Al Jazeera's Tony Cheng, reporting from Beijing, said.
"Now China is profoundly concerned about the regime in Pyongyang, which seems increasingly unstable and seems increasingly not to follow Beijing's lead."
Japan is expected to impose its own sanctions on North Korea, including suspending all trade, in a largely symbolic demonstration of its opposition to the test, the Kyodo news agency reported.
Al Jazeera's Cheng said that it was difficult to judge what effect the new sanctions would have on the already impoverished state.
"Their finances are in big trouble. They have almost nothing that anybody else wants to buy but these arms"
executive vice-president of the Asia Society
"This is really just tightening sanctions that already exist on North Korea, but they do target it in specific areas," he said.
"I think that one area that will hurt quite a lot will be the ban on conventional weapons arms sales and the possibility of stopping ships going to and from North Korea ... that is a business that could earn Pyongyang as much as $100m."
Jamie Metzl, the executive vice-president of the Asia Society, said North Korea had exported arms to about 20 countries in the past, including Iran, Egypt, Pakistan, Myanmar, Zimbabwe and Sudan.
"Their finances are in big trouble. They have almost nothing that anybody else wants to buy but these arms," Metzl said.
The UN vote comes amid continuing tensions on the Korean peninsula after North Korea on Thursday demanded a 3,000 per cent increase in rent and a 400 per cent increase in wages for 40,000 workers employed by South Korean companies at an industrial park in the North Korean border town of Kaesong.
North Korean state media issued a statement on Thursday saying that relations between the two countries had reached the "phase of catastrophe" and that the Kaesong complex had been "thrown into a serious crisis".