The index also tracks a fall in America's ability to compete in a lower emissions world during the first few years of President Barack Obama's time in office.
Nineteen economic, energy and industrial indicators were used to calculate a country's carbon competitiveness. The updated ranking includes new data from 2008 to 2010, and indicators used include emissions growth, energy generation and the make-up of export industries.
Australia ranks 17th out of 19 countries for low-carbon competitiveness - above only India and Saudi Arabia. It fell one place from a year ago as Indonesia leapfrogged a number of nations.
But due to a lag in data Australia's position does not take into account the national carbon price and associated programs introduced last July.
Climate Institute chief executive John Connor said that while the carbon price was working, Australia's ranking was unlikely to have improved significantly in the first year of operation because of uncertainty over the scheme's future. He said Australia's position was unlikely to significantly improve until 2014.
''I don't expect that ranking to have changed a great deal in the first year it has now come in,'' he said. ''It is actually about how we start to boost it with the [$10 billion] Clean Energy Finance Corporation and greater certainty [around the carbon price].''
The survey shows the biggest movers between 2008 and 2010 were China and Indonesia, which both moved up four spots to third and 14th respectively.
The report says the rapid rise of China is attributable to increases in clean energy investment and high-technology exports. If China had maintained its clean energy investment at 2008 levels, it would be in eighth place, the report says.
It says Asia is on track to replace Europe as the world's largest clean energy investment region, capturing more than a third of the world's investment in 2012.
Clean energy powerhouse Germany fell from second to sixth. The US fell from ninth to 11th due to declining high-tech exports and a surge in reliance on air freight.
France remained the top country on the index due to its relatively low-emission and energy-efficient economy and high-technology exports. It is followed by Japan and then China. South Korea and Britain round out the top five.