The Chinese Shanghai Composite fell 0.49 percent or 10.78 points to 2190.57. Hong Kong's Hang Seng declined 0.34 percent or 67.01 points to 19742.12. Major losers were CNOOC Ltd (1.53 percent) and PetroChina Co Ltd (1.61 percent).
Japan's Nikkei Stock Average fell 0.36 percent or 32.34 points to 9047.46. Among major losers were NEC Corp (3.28 percent), Fujitsu Ltd (3.14 percent) and Teijin Ltd (2.87 percent).
South Korea's KOSPI Composite Index declined 0.70 percent or 13.17 points to 1861.40. Shares of Samsung Electronics Co Ltd fell 1.69 percent and shares of Hyundai Motor Co declined 1.93 percent.
India's BSE Sensex fell 0.26 percent or 45.28 points to 17493.39. Major losers were Thermax Limited (2.53 percent), Infosys (0.96 percent) and OMGC (0.82 percent).
The ECB said in Frankfurt Thursday that it had decided to cut the main interest rate to 0.75 percent in an attempt to rejuvenate the economic growth momentum. But market players were disappointed with the central bank's move to not pursue any bolder stimulus measures for now.
In all, then, it looks like the ECB's role in responding to the sovereign debt crisis is over for now and the onus remains firmly on euro-zone governments to provide enough money to backstop the periphery, Jennifer McKeown, an economist at Capital Economics, said.
Also the Bank of England decided to add a further 50 billion pounds ($78 billion) to its quantitative easing program.
The People's Bank of China (PBC) Thursday cut interest rates for a second time this year. The central bank cut the main lending rate by a slightly-larger 31bps, taking it to 6 percent. Market participants were rather discouraged by this decision as it hints at an uncertain economic growth in the world's second largest economy.