The damage was mostly superficial with MSCI's index of Asia-Pacific shares outside Japan off just 0.3%. Shares in Shanghai lost 0.7% while Japan's Nikkei eased 0.4%.
Helping sentiment was the Bank of Japan's decision to stick with its massive stimulus program that has shown tentative signs of breaking the grip of deflation.
Indeed, a survey of Japanese manufacturing out on Thursday showed activity accelerated to its fastest in more than three years in September.
There was also upbeat news from Australia where approvals to build new homes surged to their highest since early 2010, concrete evidence that record-low interest rates were working to support economic growth.
These factors helped lessen the drag from Wall Street, which had slipped after the US central bank kept its $85 billion-a-month stimulus plan intact but did not sound quite as alarmed about the state of the economy as some had anticipated.
Given US shares had reached record highs this week, the resulting profit-taking came as no surprise.
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The Dow Jones industrial average fell 0.39% and the S&P 500 lost 0.49%. The MSCI world equity index showed even less damage, easing just 0.1% from a high not seen since January 2008.
Dealers said the market had talked itself into expecting the Fed would make dovish changes to the statement, so it was somehow considered "hawkish" when those did not materialise.
"We interpreted the statement as neutral and balanced and think the Fed is essentially in a holding pattern," said analysts at Australia and New Zealand Bank.
"If anything, the assessment section was a touch softer, suggesting the Fed are not trying to give the impression that it is setting up for a December move."
STILL EYEING MARCH
Much of the market is still not pricing in a start of tapering until March, when the Fed policy meeting will include new economic forecasts from officials and a news conference by Chairman Ben Bernanke.
It was notable that Fed funds futures barely budged on the statement, showing investors still did not expect any increase in official rates until well into 2015.
Likewise, short-dated Treasury yields stayed well anchored while the longer end moved up only modestly. Yields on the 10-year note were steady at 2.53%, and far below the 3% peak hit in early September.
Currency moves were also moderate, with the US dollar edging further away from recent lows. The dollar index edged fractionally higher on the day to 79.814.
The euro dipped to $1.3713, losing gains made Wednesday after data showed a jump in euro zone sentiment in October. The dollar fared better against the yen to reach 98.44, a move that offered some support to Japanese stocks.
There was more action in the New Zealand dollar which bounced after the country's central bank said increases in interest rates were still likely to be needed next year, putting it well ahead of most other developed economies in tightening.
The currency rallied as much as half a US cent in reaction, though the central bank also noted that a strong currency meant it might be able to wait longer before having to raise rates.
In commodities, spot gold faded after rising the most in a week at one stage on Wednesday. Gold fetched $1,338.73 an ounce, down from a high of $1,359.16.
Brent crude eased 25 cents to $109.61 a barrel but that followed gains on Wednesday as export disruptions in Libya continued to cut supplies to Europe and Asia.
The benchmark US contract was off 22 cents at $96.55 a barrel after a bigger-than-expected increase in inventories in the United States.