Russia and China said the proposed draft was "unbalanced".
The document was rejected just hours after activists accused Syrian troops of killing at least 55 people in Homs.
The BBC's Paul Wood, who entered the Syrian city with rebels after the vote, says gun and shell fire can be heard there.
On Sunday, opponents of the Syrian government ransacked the country's embassy in the Australian capital, Canberra.
At the sceneIn broad terms, Russia's decision was coloured by a decades-long alliance with the Assad regime, and by their policy of non-intervention in the affairs of a sovereign state.
But there were two other reasons why they refused to accept this specific resolution.
First of all, they were never happy with the way it came about. They supported the Arab League observer mission despatched to Syria in December, but they didn't think its conclusions warranted the subsequent league decision to promote a political process that in essence saw Mr Assad step aside.
Rather, the Russians suspected that the observer mission had been hijacked by Qatar and Saudi Arabia backed by Western powers, and that their proposal was a thinly disguised attempt at regime change.
Secondly, the Russians highlight the element of armed conflict in the violence, rather than simply focusing on government repression of civilians. They say the Security Council should also be making demands of the armed opposition, not just the regime, or it will be taking sides in a civil war.
'Disgusted' American UN envoy Susan Rice described the veto on Saturday as "shameful", saying Russia and China aimed to "sell out the Syrian people and shield a craven tyrant".
"Any further bloodshed that flows will be on their hands," she said.
She later wrote on Twitter: "Disgusted that Russia and China prevented the UN Security Council from fulfilling its sole purpose."
Britain's Foreign Secretary William Hague said in a statement that the approach by Moscow and Beijing "lets the Syrian people down, and will only encourage President [Bashar] Assad's brutal regime to increase the killing".
In Paris, French President Nicolas Sarkozy said in a statement that he "strongly deplores" the veto but promised to carry on seeking a solution.
Mohammed Loulichki, Morocco's ambassador to the UN and the sole Arab member of the current council, voiced "great regret and disappointment" that Moscow and Beijing had struck it down.
The Arab draft resolution had adopted an Arab League call for a "Syrian-led political transition to a democratic, plural political system".
However, Russia said it singled out the government and did not contain measures against armed opposition groups.
Russia's UN envoy Vitaly Churkin said the draft had lacked balance.
Beijing's UN ambassador Li Baodong said putting pressure on the Syrian government or "imposing a solution" would not help to resolve the issue.
Pro-Assad residents in the Syrian capital Damascus welcomed the Sino-Russian stance.
"I believe there are more important issues for the Security Council to take care of... such as the starvation in Somalia, and Gaza," one told BBC News.
'Hysterical campaign' Early accounts of the casualties in Homs on Saturday talked of as many as 200 deaths, but one of the main activist groups later revised its confirmed toll down to 55.
The BBC's Paul Wood says he and his cameraman heard heavy machine-gun fire and explosions when they entered Homs on Saturday afternoon.
He says Homs appears to have come under a pretty relentless bombardment and parts of the city that oppose the regime have been cut off.
Homs was one of the first cities to join anti-Assad protests, and became one of the focal points of dissent after government forces fired on crowds in April last year. Many army defectors have sought refuge in the city.
State media dismissed the Homs casualty reports as a "hysterical campaign of incitement" by armed gangs designed to influence the UN.
International media outlets are restricted in Syria, making it difficult to verify the claims of either side.
Syria has been gripped by nationwide protests against Mr Assad's government for almost a year, in a struggle that has claimed at least 5,400 lives, according to the UN.
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