The report also singled out emerging powers India, Brazil and South Africa, saying they were "complicit through their silence" on key rights issues.
"You've had people standing up, putting their lives on the line," Amnesty's Secretary General Salil Shetty told AFP.
"Unfortunately that has been met by a complete failed leadership both at the national and global level," he told AFP.
Shetty said that in the 21st century the UN Security Council was "simply not fit for purpose. If they do not change the way in which they behave, I think there are going to be increasing questions about the relevance of the body."
In its 50th annual report, Amnesty said the vocal support by many global powers in the early months of the Arab Spring in 2011 had not translated into action, with many international leaders now looking the other way.
In Syria the group said there was a "clear and compelling case" for alleged crimes against humanity by Bashar Al-Assad's regime to be referred to the International Criminal Court.
"The determination of some UN Security Council members to shield Syria at any cost leaves accountability for these crimes elusive and is a betrayal of the Syrian people," said Shetty.
Russia and China have vetoed two Council resolutions which condemned Assad, and they fiercely oppose UN sanctions.
"Two countries that are among the top six arms dealers in the world, who are permanent members of the Security Council, may have been voting much more with their pocket in mind," said Widney Brown, senior director of international law and policy at Amnesty.
Amnesty said it was the conference on a global treaty limiting the arms trade in July that would really show whether UN member states were willing to take on serious challenges.
The conference is set for July 2-27 in New York. It follows an agreement in 2009 by most of the world's major weapons exporters, including the United States, to seek a treaty that strengthens controls on the trade.
"The UN meeting to agree an Arms Trade Treaty in July will be an acid test for politicians to place rights over self-interest and profit," the Amnesty report said.
"Without a strong treaty, the UN Security Council's guardianship of global peace and security seems doomed to failure; its permanent members wielding an absolute veto on any resolution despite being the world's largest arms suppliers."
The UN General Assembly passed a resolution in 2006 calling for such a treaty, but the United States, the world's biggest exporter of weaponry, voted against it, the only country to do so.
The report also focused on other areas, including:
- China, which Amnesty said had thrown the "full weight" of its security apparatus into suffocating protests.
- Russia, where civic activism grew amid the biggest protests since the Soviet Union, but opposition voices were "abused and systematically undermined."
- Myanmar, where the government allowed Nobel Peace Prize winner Aung San Suu Kyi to stand in elections and freed hundreds of political prisoners, although fighting with ethnic groups and fresh detentions showed "limits to the reform".