"While there was applause for the (Fed) cuts we saw yesterday, investors are now standing back and reflecting further on what that means," said Keith Bowman, an analyst at Hargreaves Lansdown Stockbrokers.
"Some nervousness has been expressed in the currency markets. We have seen a weakened dollar, which has probably had an effect on the markets across the board," he added.
The dollar fell from 88.96 yen to 88.33 yen, trading as low as 88.22 yen, near a 13-year low. The euro strengthened further to $1.4075 in European morning trading. The euro had gone as high as $1.4148 late Tuesday, its highest point since Oct. 1.
In Asia, markets climbed higher. Japan's Nikkei 225 stock average rose 44.50 points, or 0.5 percent, to 8,612.52 after initially rising 1.1 percent, and Hong Kong's Hang Seng Index rose 2.2 percent to 15,460.52.
South Korea's Kospi added 0.7 percent to 1,169.75, while benchmarks in Thailand and Australia also gained. However, China and Singapore stocks closed largely flat and India's benchmark lost ground.
Investor enthusiasm was tempered by a mix of lingering worries about the U.S. economy and a weakening dollar that threatened to add to the woes of Asia's exporters. Also weighing on markets was a steep drop in U.S. stock futures, suggesting Tuesday's rally on Wall Street would quickly fizzle.
Overnight, the Dow Jones industrials surged more than 4 percent after the Fed cut its target rate for overnight loans between banks to a range of zero to 0.25 percent and pledged to use "all available tools" to heal the U.S. economy.
The central bank's bold actions surprised Wall Street - most analysts expected a 0.5 percentage point cut rather than 0.75 - and raised hopes of lower interest rates and cheaper money around the world to get companies and consumers spending again. In Asia, Hong Kong's central bank followed suit with its own rate reduction, while speculation mounted of further monetary easing from the Bank of Japan on Friday.
"Every central bank is pumping loads of liquidity into the markets and this is very positive for the markets," said John Mar, co-head of sales trading of Daiwa Securities SMBC Co. in Hong Kong.
Trade was far more cautious than in the U.S., where markets soared on the Fed's move. The Dow rose 4.2 percent to 8,924.14 and the broader Standard & Poor's 500 index advanced 5.1 percent to 913.18.
Dow futures were down 173 points, or 1.9 percent, at 8,741 and S&P500 futures were off 22.40 points, or 2.5 percent, at 890.40.
Analysts said the Fed's indications that it would do whatever is necessary to help bring an end to the longest economic contraction in a quarter-century underscored just how deep America's recession is.
"Investors in Asia have less confidence than their American counterparts in the Fed's ability to engineer an economic recovery," said Dariusz Kowalczyk, chief investment strategist for CFC Seymour in Hong Kong.
Tokyo's gains were limited by the souring dollar and worries about Honda, whose shares slid 4.2 percent.
Japan's No. 2 automaker said late in the day it was slashing its profit forecast for the fiscal year and cutting managers' pay amid a global downturn in the auto industry. Nissan Motor Co. fell 4.1 percent after announcing plans to scale back production by a further 78,000 vehicles and cut 500 temporary workers.
In Hong Kong, investors sent property firms surging after the territory's de facto central bank followed the Fed's move by cutting its base rate by a full percentage point to 0.5 percent. Because the territory's currency is pegged to the dollar, the Hong Kong Monetary Authority's actions usually track the Fed's.
Oil prices rose, with light, sweet crude for January delivery up $1.66 to $45.26 a barrel in European trade as investors awaited official confirmation that OPEC has decided to cut output sharply.
The contract fell 91 cents to settle at $43.60 a barrel overnight.
Saudi oil minister Ali Naimi said Wednesday that there was consensus among OPEC members, who account for about 40 percent of global supply, to cut production by 2 million barrels per day from Jan. 1.
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AP business writer Jeremiah Marquez contributed to this report from Hong Kong.
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