An EU body, the agency plans to push for legislation for more use of market-based instruments to change behaviour among signatory countries.
Its 2004 report, published on Tuesday, documents worrying levels of urban air pollution and agricultural contamination of water, and increasing amounts of packaging and other waste.
Its evidence for climate change comes from receding glaciers, disturbance of marine species, and rising energy consumption.
Suggestions for change
Among its recommendations, it says ways to tackle the issues include increasing energy efficiency, greater use of renewable energy, and the ever-unpopular "rethinking options for transport".
The report says the number of weather and climate-related disasters in Europe during the 1990s was double the figure of the previous decade.
Their average cost "is conservatively estimated at around 10bn euros (£6.7bn) per year and rising".
The agency's executive director, Professor Jacqueline McGlade, said: "Such figures suggest that managing Europe's natural resources is increasingly important for ensuring the viability of Europe's economic and social capital.
"Overall trends in waste generation are unsustainable"
European Environment Agency, 2004 report
Other findings in the report found that nitrate pollution from farming is continuing, and there is evidence that consumers are paying most of the clean-up costs for drinking water.
Much of the continent's urban population is still exposed to air pollution above health protection levels, with low-level ozone and particulates the main concerns.
Packaging waste is rising, and is projected to continue doing so, the report added. "Overall trends in waste generation are unsustainable and current policy tools inadequate".
The agency's 31 members are the 25 EU states, the three EU candidate countries - Bulgaria, Romania and Turkey - and Iceland, Liechtenstein and Norway. Membership negotiations are under way with Switzerland.