2014 was a year of "catastrophic" conflict, said Amnesty, with large-scale destruction such as in the city of Kobane in northern Syria
Amnesty International has urged the five permanent members of the UN Security Council to give up their power of veto in cases where atrocities are being committed.
In its annual report, the rights group said the global response to an array of catastrophes in 2014 had been shameful.
Richer countries were guilty of taking an "abhorrent" stance by not sheltering more refugees, Amnesty said.
The outlook for 2015 was bleak, the group added.
Saying that 2014 had been a catastrophic year for victims of conflict and violence, Amnesty said world leaders needed to act immediately to confront the changing nature of armed conflict.
'Miserable failure'
Salil Shetty, the organisation's secretary general, said in a statement that the United Nations Security Council had "miserably failed" to protect civilians.
Instead, the council's five permanent members - the UK, China, France, Russia and the US - had used their veto to "promote their political self-interest or geopolitical interest above the interest of protecting civilians," Mr Shetty said.
Part of the solution would be those countries surrendering their Security Council veto on issues related to mass killing and genocide, Amnesty added.
Last year, the veto was only used twice in the UN Security Council.
In March, Russia vetoed a resolution condemning as illegal a referendum on the status of Crimea and in May Russia and China blocked a resolution condemning Syria.
But many draft resolutions proposing tough action to deal with crises never reach the voting stage because they would almost certainly be vetoed, says the BBC World Affairs correspondent Mike Wooldridge.
The Amnesty report argues that if the use of the veto in the Security Council had already been restrained in the way the report suggests, that could have made it impossible to block UN action over the violence in Syria.
This might have resulted in President Bashar al-Assad being referred to the International Criminal Court, greater access for badly needed humanitarian aid would have been possible and civilians helped more,writes Mike Wooldridge.
The initiative to suspend the veto right in particular circumstances was first raised 15 years ago and may be gathering momentum, but it is still unclear when it might have enough backing to be enforced, our correspondent adds.
Suspension mechanism
One key question is who would decide when a crisis situation warrants a suspension of the veto right.
Amnesty International's Senior Director for Research Anna Neistat told the BBC inquiries by the UN Commission for Human Right or the International Criminal Court could determine what constitutes a crime against humanity for example.
When asked if these mechanisms would be fast enough for action to be taken in time, she cited the international intervention in Libya in 2011 and the green light for cross-border humanitarian assistance to Syria in 2014 as examples where they did work.
The UK government has not yet made a specific commitment in favour of the voluntary renunciation of the veto.
But the Foreign Office said in response to the Amnesty report: "The United Kingdom wholeheartedly supports the principle that the Security Council must act to stop mass atrocities and crimes against humanity.
"We cannot envisage circumstances where we would use our veto to block such action."
Islamic State fighters were behind many of the atrocities in 2014
Nigerian Islamists Boko Haram have created instability in West Africa
Hundreds of Yazidi refugees were forced to flee Islamic State in Iraq last year
Amnesty's report said that 2014 had led to one of the worst refugee crises in history, with four million Syrians displaced by war and thousands of migrants dying in the Mediterranean.
The group criticised the response of European leaders to the crisis.
It said the efforts of wealthy countries to keep refugees out took "precedence over their efforts to keep people alive".
Amnesty also used its report to urge governments to adhere to a worldwide agreement on arms.
A global treaty came into force last year and aims to regulate the arms industry by controlling the supply of weapons to criminal groups.
