Moscow's UN envoy, Vitaly Churkin, said the resolution was one-sided and supported the armed opposition.
Russia has criticised a UN General Assembly resolution on Syria, calling it "blatant" support for rebel groups battling President Bashar al-Assad.
Russia voted "no" on Friday along with China, Syria, Cuba, Iran, North Korea, Belarus, Bolivia, Nicaragua, Burma, Zimbabwe and Venezuela. Among those states abstaining were India and Pakistan.
Vitaly Churkin, Russia's UN ambassador, said on Friday that the main backers of the resolution, overwhelmingly passed by the UN assembly, were providing "mercenaries and arms" to the Syrian opposition.
He said the resolution, which condemned Assad's government and the UN Security Council's failure to act on the Syrian crisis, would not halt the civil war.
"Behind the facade of humanitarian rhetoric, the resolution hides a blatant support for the armed opposition," Churkin told the assembly.
Without naming them, he said the "most active" backers of the resolution "are actively supporting and financing" the opposition and "giving them mercenaries and arms". Saudi Arabia drew up the resolution with strong support from other Arab and western nations.
Russia and China have three times vetoed UN Security Council resolutions which could have led to sanctions against Syria, and Churkin also criticised the attack on the Security Council's failure to act in Friday's resolution.
In Syria, government forces backed by tanks launched a new assault in Damascus while shelling continued in the country's largest city, Aleppo.
Activists say more than 20,000 people - mostly civilians - have died in 17 months of unrest.
Fighting raged in the Tadamon district of Damascus for a second day on Friday, with opposition activists saying government troops had regained control of the area.
Eyewitnesses and activists say government forces used dozens of tanks and armoured vehicles to attack what had been seen as the rebels' last stronghold in the capital.
Troops killed "several" rebels and wounded many more, Syrian state media reported.
Fighting has also continued in Aleppo, where government forces have been trying to reclaim areas seized by the Free Syrian Army (FSA) in the past two weeks.
Hundreds of people gathered in the al-Shaar neighbourhood to chant "The people want the execution of Bashar!" and "The people want freedom and peace", AFP news agency reporter at the scene says.
UN peacekeeping chief Herve Ladsous told the Security Council that UN observers in Aleppo were seeing "a considerable build-up of military means, where we have reason to believe that the main battle is about to start".