On Friday, China and Russia vetoed the resolution calling on Myanmar's military junta to stop persecution of minority and opposition groups.
It urged Myanmar to release political prisoners, move towards democracy and stop attacks against minorities, many of whom are used for forced labour.
The US, which softened the draft from the original, received backing from nine of the 15 nations on the council.
But among the other six were China and Russia, permanent council members with veto rights.
South Africa also voted "no" while Qatar, Indonesia and Congo Republic abstained.
Voting with Washington were Britain, which co-sponsored the draft, France, Belgium, Italy, Ghana, Peru, Panama and Slovakia.
No regional threat
"The situation in Myanmar does not constitute a threat to regional and international peace and security," Liu Jianchao, of the Chinese foreign ministry, said in Beijing, according to the official Xinhua news agency on Saturday.
"If the Security Council passed a resolution on the Myanmar issue, that would have exceeded the duties of the Council laid out in the United Nations Charter."
Beijing's criticisms of it were echoed by the Indonesian foreign minister, who said his views reflected other Southeast Asian countries.
"The case would be more appropriately brought to the attention of the human rights council rather than the UN Security Council," Hassan Wirajuda said.
Emyr Jones Parry, Britain's UN ambassador, said he helped push the resolution because "I want tomorrow morning to be able to reassure myself that we did the right thing, the right thing by the people of Myanmar".
The military has run Myanmar since 1962, ignoring a 1990 landslide election victory by the National League for Democracy party led by Aung San Suu Kyi, a Nobel laureate, who has been in prison or under house arrest since then. Thousands of her supporters have been jailed.
The US measure called for the release of Suu Kyi and all other political prisoners and for her party and all other groups to be able to operate freely.
No one denied abuses by Myanmar's junta, which has been condemned in the 192-member General Assembly. At issue was whether rights violations are a danger to peace and security in the region, the council's mandate.
Otherwise, human rights violations are an issue for the assembly, whose resolutions carry less weight.