She said that Washington's decision to arm rebel groups was a poor substitute for forging a peace plan that the UN Security Council will unite behind.
"I haven't seen a situation where more arms leads to more opportunities for negotiations [towards a resolution]. Not to mention what this might mean for the rise of extremism," she said.
While the European Commission would continue its unprecedented aid effort, global humanitarian resources were finite. A political resolution must be reached before Lebanon or Jordan or both were stretched to breaking point and the crisis deepened exponentially, Georgieva said.
"It is so disappointing to see the international community sleepwalking into this disaster," she said.
"Any time there is a new eruption of fighting we hope it will be the wake-up call. But obviously this hasn't happened yet."
The G8 leaders failed to advance the chances of peace this week. The deepening division between Russian and Western allegiances within the Security Council means an international peace conference on Syria that was due to take place in Geneva this month has now been delayed until August at the earliest.
To date, at least 1.66 million Syrians have fled the bloodshed to neighbouring countries, with Jordan, Lebanon, Turkey and Iraq bearing the brunt.
The European Commission has led an unprecedented aid effort to provide material and strategic support to the governments buckling under the weight of their swelling refugee populations.
But as the conflict rumbled on with little sign of abating and the numbers of refugees rose with each week, the gap between humanitarian capacity and need grew, Georgieva warned.
Before the Syrian conflict, Jordan was already host to a vast community of Palestinian and Iraqi refugees, and suffered from chronic water shortages.
In the past two years, it has accommodated an estimated 450,000 Syrian refugees. At least half a million more are waiting to be registered in Lebanon, where sectarian tensions simmer perilously close to civil unrest.
Stressing that half of the refugees fleeing Syria were children, many of whom had now been out of school for two years, Georgieva warned that it might already be too late to avert the imminent danger to regional security from a generation of children "with no jobs but with guns in their hands".
"We are now looking at more than 100 self-proclaimed rebels groups who want to be part of a negotiating party. The longer we postpone, the more detrimental the delay will become," she added.
On the ground in Syria, government forces reinforced with Iranian-led Hizbollah fighters surged into Aleppo and the suburbs of the capital Damascus yesterday, attempting to build upon their recent successes in the country's south. Activists reported fierce gun battles in the alleyways of the Old City.
The British-based Syrian Observatory for Human Rights also reported clashes in Homs, Hama, Deraa and Damascus.
Opposition groups responded with an operation to seize control of a major highway running from Aleppo to the Turkish border - an effort bolstered by the arrival of a shipment of Konkurs anti-tank missiles in Aleppo.
