The country's foreign ministry said in a statement on Tuesday that South Korea will continue to strengthen cooperation with the international community to ensure that the resolutions "are thoroughly implemented".
"North Korea should accept the strict warning from the international community that continued provocations only deepen the diplomatic isolation and economic pressure," the ministry said.
On Monday, the 15-member council - which does not include South Korea - adopted a US-drafted resolution imposing fresh punishing measures against North Korea following its sixth and largest nuclear test on September 3.
The council voted 15-0 for a ban on textile exports and restriction of shipments of oil products to North Korea.
Shinzo Abe, Japan's prime minister, also welcomed the move, describing it as "a remarkably tough sanctions resolution".
"It is important to put an unprecedented level of pressure on North Korea to make it change its policies," Abe said. Japan is a member of the council.
On Tuesday, North Korea lashed out at the UNSC, describing the sanctions as "vicious" and condemning the move in "the strongest terms".
"Yesterday the Washington regime fabricated the most vicious sanctions resolution," Pyongyang's ambassador in Geneva told the UN Conference on Disarmament in the first North Korean reaction to Monday's unanimous vote.
Though the resolution was backed unanimously, the final document was a watered-down version of the original US proposal following pressure from China and Russia.
Al Jazeera's James Bays, reporting from the UN in New York City, said that both China and Russia "made it very clear that they don't believe everything is being done that should be done".
He said that both countries "believe there are other things that have to happen, including some that the Trump administration won't like".
China has held the position that stronger sanctions would not be helpful in halting North Korea's nuclear programme.
A Chinese state media editorial on Tuesday said the US should stop isolating North Korea and return to the table for talks.
"The ultimate goal of these moves should be to bring the country back to the negotiating table so that all sides concerned can sit together and settle the terms that can actually freeze or terminate DPRK's [Democratic People's Republic of Korea] nuclear plans, and ensure a lasting and sustainable peace in the region," the Xinhua news agency editorial said.
Since Kim Jong-un's ascendancy in December 2011, North Korea has accelerated its missile development programme.
Source: Al Jazeera and news agencies