The ECB cut its deposit rate by the minimum 0.1 percentage point to -0.3%, and extended its asset purchase program, but did not increase its monthly government bond purchases.
Investors were expecting a bigger cut in the rates, analysts said.
Japan's benchmark Nikkei 225 index was down 1.7% to 19,606.32 points.
Evan Lucas, market strategist at trading firm IG said Friday's shares sell-off is because there was over-excitement and high expectations for what the ECB would deliver at its policy meeting.
"I have been fully aware that last night's ECB meeting would be the biggest 'disappointment' event of the week," he wrote in a note.
The six month extension of its stimulus program was seen as the bare minimum, because traders were looking for a one-year extension of the plan - or even an open-ended plan.
"What the market 'wanted' versus what the market was 'going to get' were two distinctly different events," Mr Lucas said.
Chinese markets followed global markets lower with Shanghai Composite index down 1% to 3,549.51, while Hong Kong's Hang Seng index lost 1.2% to 22,158.57.
Australia's S&P/ASX 200 index was down 1.7% to 5,138 despite retail sales rising 0.5% in October from the month before.
It was the third month of solid growth as shoppers spent big on household goods and at department stores.
South Korea's Kospi index was down 0.8% to 1,978.78 points.
Asian shares opened lower following the global trend as investors reacted negatively to the European Central Bank's (ECB) policy-easing moves.