Europe's economic motor, Germany, returned to growth but still disappointed. Its gross domestic product rose 0.1 percent in the first quarter of the year. That's less than the 0.3 percent rise analysts were expecting. Meanwhile, the French economy, the bloc's second-largest, fell back into recession.
Those figures stand is stark contrast to growing signs of a rebound in the United States that drove Asian shares up earlier in the day.
In morning trading in Europe, France's CAC-40 index was down 0.2 percent to 3,958, while the DAX in Germany fell 0.1 percent to 8,332. Britain's FTSE index of leading shares dropped 0.2 percent to 6,672.
U.S. markets also looked likely to open down. Dow futures slumped 0.1 percent to 15,161, while S&P futures fell 0.2 percent to 1,645.
While positive earnings reports could turn the tide later in the day, analysts said, the outlook for the European economy will continue to be bad.
"The upside for domestic demand in the eurozone remains constrained by restrictive fiscal policy in many countries, still tight credit conditions, high and rising unemployment, and limited consumer purchasing power despite general very low inflation," said Howard Archer, IHS Global Insight's chief European economist. "Meanwhile, global growth is relatively muted and currently stuttering, which is constraining eurozone exports."
Earlier, Asian stocks focused instead on an improving U.S. economy. On Tuesday, a report from the National Federation of Independent Business showed a slight improvement in confidence among small business owners in the U.S. in April.
Japan's Nikkei 225 index surged 2.3 percent to close at 15,096.03, propelled by a falling yen and a surge in Sony's shares.
Hong Kong's Hang Seng rose 0.5 percent to 23,044.24. South Korea's Kospi added 0.1 percent to 1,971.26. Benchmarks in India, Thailand, Singapore and Taiwan also rose. Australia's S&P/ASX 200 shed 0.6 percent to 5,191.70.
But the poor European data was weighing on oil prices since a slowing economy uses less energy. Benchmark oil for June delivery fell 70 cents to $93.51 per barrel in electronic trading on the New York Mercantile Exchange.
In currencies, the euro fell to $1.2885 from $1.2937 late Tuesday in New York.
Pamela Sampson contributed to this report from Bangkok.