The two countries are "failing the people of Syria," said Britain's U.N. Ambassador Mark Lyall Grant, who was first to speak at the Security Council meeting after the vote. "The effect of their actions is to protect a brutal regime."
Russia and China, which have major trade deals with Syria, have said they want more balanced resolutions that call on all sides to halt the violence.
Grant accused them of putting "their national interests ahead of the lives of millions of Syrians." And he said they are relying on al-Assad's "broken promises."
It marked the third time in 10 months that the two countries blocked tough resolutions focused on al-Assad's regime.
Susan Rice, the U.S. ambassador to the United Nations, said those two countries' previous two vetoes were "very destructive," and that this latest one is "even more dangerous and deplorable."
"Despite paranoid, if not disingenuous, claims to the contrary, it would in no way authorize nor even pave the way for foreign military intervention" she said.
The resolution would have given the U.N. mission to Syria "a fighting chance to accomplish its mandate," she argued.
Russia shot back that the vote should never have taken place.
Russia had "very clearly and consistently explained" that it would not accept a resolution that "would open the path for pressure of sanctions and further to extend military involvement in Syrian domestic affairs," said Vitaly Churkin, Russia's ambassador to the United Nations.
Western diplomats "could have done something, anything, to promote dialogue" rather than "fan the flames of extremists," he said.
He described the draft resolution as "biased," saying it threatened sanctions exclusively at the Syrian government.
China's U.N. Ambassador Li Baodong said his country is also "highly concerned" about the violence, but the draft resolution was "seriously problematic," because it intended to pressure only one side in the conflict. It would not help resolve the issue, "but derail the issue from the track of political segment," further aggravating turmoil, he argued.
Syria's U.N. Ambassador Bashar Jaafari slammed the council for not issuing an official condemnation of Wednesday's bombing, although he noted that Kofi Annan, joint envoy to Syria for the United Nations and the Arab League, condemned it.
The lack of an official condemnation by the council indicates that talk of "supporting a peaceful solution in Syria is but a slogan," argued Jaafari.
He said the "Syrian people alone" should decide their future "without foreign intervention."
He rejected a "misleading picture" of Syria as a tyrannical regime killing its people and said a solution should be found through a "political process that satisfies the Syrian people." All will participate to help "establish democracy" and "free elections," he insisted.
The al-Assad family has ruled Syria for more than 40 years.
When asked later about Jaafari's complaint, France's U.N. Ambassador Jean-Hugues Simon-Michel said, "We have always condemned terrorism, so I think there is no ambiguity." He added that the attack highlights the need for an end to the bloodshed.
At least 94 people were killed Thursday, including 25 in Damascus suburbs and 13 inside Damascus, the opposition Local Coordination Committees of Syria said. The Damascus suburb Qaboon was under heavy fire Thursday, according to an opposition activist.
Residents trying to flee the violence have nowhere to go because clashes are raging in most of Damascus province, said Omar al-Dimashki, a spokesman for the Revolution Leadership Council of Damascus.
"It is surrounded by tanks, and anything that moves is currently being shelled, and rockets are falling on the homes," he said.
Syria, which blames the violence on "armed terrorist groups," said it "repelled" some groups that attempted to enter Syria from Lebanon on Wednesday night.
The regime said Wednesday's bombing was carried out by people "implementing foreign plots."
The Syrian military issued a statement stressing its "resolution to decisively eliminating the criminal and murder gangs and chasing them out of their rotten hideouts wherever they are until clearing the homeland of their evils," said state-run news agency SANA.
Anyone who thinks that targeting leaders will "twist Syria's arms is 'deluded,'" the statement said, according to SANA.
The officials killed in the blast were the defense minister; the deputy defense minister, who is the president's brother-in-law; and al-Assad's security adviser and assistant vice president, state TV reported.
The deputy head of the rebel Free Syrian Army, Col. Malek al-Kurdi, said the attack was coordinated by rebel brigades. Some other rebel commanders say it's unclear who was behind the attack.
As violence has raged in what the Red Cross now declares to be a civil war across the country, world leaders have stepped up diplomatic efforts.
Annan traveled to Moscow this week in hopes of winning support from Russia for tough action at the Security Council.
U.S. President Barack Obama called his Russian counterpart, Vladimir Putin, to discuss the Syrian situation, the White House said in a statement Wednesday.
Thursday's Security Council vote showed those diplomatic efforts had failed.
Western countries were pushing for a resolution that threatened new sanctions if government forces don't stop attacks against civilians.
Pakistan and South Africa abstained from voting.
The resolution also called for renewing the 300-member U.N. observer mission for 45 days after it was suspended because of violence.
Russia put forward its own draft, which "strongly urges all parties in Syria to cease immediately all armed violence in all its forms."
Since the crisis began in March 2011, the United Nations estimates, more than 10,000 people have been killed in the violence; the opposition Local Coordination Committees of Syria estimates that more than 16,000 have died.
CNN cannot independently confirm reports of violence in the nation because the government restricts access by foreign journalists.
Intellpuke: You can read this article by CNN Correspondent Josh Levs in context here: edition.cnn.com/2012/07/19/world/meast/syria-unrest/index.html?hpt=hp_t1
CNN's Arwa Damon, Richard Roth, Brian Walker and Salma Abdelaziz contributed reporting to this news article.