At 2100 GMT, the euro was down more than one percent against the greenback, trading at $1.2391 from 1.2527 Wednesday.
The safe-haven yen also gained on the euro, trading at 99.00 per euro compared with 100.05 yen a day earlier.
The yen-dollar rate was virtually flat at 79.88 yen per dollar.
The Bank of China led off the action with a surprise rate cut, its second in less than a month, underscoring both the sharpness of the country's slowdown and the authorities' resolve to counter it.
The European Central Bank's cut, to a record low 0.75 percent, was on the other hand widely anticipated.
At the same time, the Bank of England kept its rate even but announced £50 billion ($78 billion, 62 billion euros) in additional stimulus.
Markets which had run up ahead of the announcements fell, with some analysts saying they were not enough and others saying they only served to highlight how dire things were.
"The frenzied action by multiple central banks at the same time... struck fear into the hearts of many traders as they sold off risk substantially," said Neal Gilbert of forex house GFT.
"After the dust settled from the easing action, the euro-dollar rate had given up all of the gains it had garnered from last week's post-EU summit rally."
"Investors had built their hopes up too high ahead of today's central bank meetings and there are growing concerns that the apparent consensus reached at last week's EU summit is not as game-changing as first thought," noted GFT's David Morrison.
The pound slipped to $1.5525 from $1.5589. The dollar was slightly higher on the Swiss franc, buying 0.9692 francs compared to 0.9588 francs on Wednesday.