Amnesty said the slim chance of being granted asylum is forcing refugees to risk their lives by undertaking dangerous boat and land crossings.
The report also alleges that those who make it to Europe are often mistreated.
"In two of the main gateways to the EU, Bulgaria and Greece, refugees from Syria are met with deplorable treatment, including life threatening push-back operations along the Greek coast, and detention for weeks in poor conditions in Bulgaria," it said.
In the latter country, Amnesty said it had found refugees "living in squalid conditions in containers, a dilapidated building and in tents."
"It is deplorable that many of those who have risked life and limb to get here are either forced back or detained in truly squalid conditions with insufficient food, water or medical care," said Shetty.
About 55,000 Syrian refugees have managed to get through and seek asylum in the EU, according to the report.
Almost 97 percent of Syria's refugees — estimated by Amnesty to be 2.3 million in total — have fled to five neighboring countries since fighting began: Lebanon, Jordan, Turkey, Iraq and Egypt.
The civil war, which has killed an estimated 126,000 people and driven millions from their homes, was sparked when the regime of President Bashar al-Assad launched a crackdown after a series of protests in March 2011.
Al Jazeera with wire services