The Fed's brighter outlook for the US economy added weight to a rally in the US dollar and put several other currencies under downward pressure.
The New Zealand dollar dropped by about US2c in response to the Fed, but several others, such as the Australian dollar and the Brazilian real, were also sharply weaker.
A more modest than expected 0.3 per cent increase in New Zealand's gross domestic product for the March quarter helped to put more downward pressure on the kiwi.
Deutsche Bank chief economist Darren Gibbs said the Fed's winding back of its so-called quantitative easing programme was not the same as tightening.
"It's just easing by less each month, and putting less stimulus into the economy," he said, adding that the Federal Reserve's latest stance was "still very data-dependent".
Sam Tuck, senior manager FX at ANZ New Zealand, said: "It is the clearest signal yet that the US is on the road out."
The kiwi's decline will be welcome news for Reserve Bank governor Graeme Wheeler, who has been trying to talk its value down for several months, persistently maintaining that the currency has been overvalued.
But at current levels, the kiwi is still higher than the Reserve Bank's perceived comfort level of around US70c.
A weaker kiwi will go down well with exporters, whose margins came under extreme pressure when the currency hit US86.75c in April, but will play havoc with importers' budgets as they pay more in New Zealand dollars for foreign goods.
By late in the trading day, the kiwi was US78.55c compared with US79.95c on Wednesday, having hit US80.5c before the Fed's announcement overnight.
The currency has dropped by 9.45 per cent since April and 11.18 per cent from its record post-float high of US88.43c in August 2011.
Dealers said any further weakness in the New Zealand dollar would depend on whether economic data from here on backed up the Fed's view that the downside risks to the outlook for the economy and the labour market had diminished.
Westpac senior currency strategist Imre Speizer said the kiwi's fall was not a "one-day wonder" and it would remain under downward pressure in the coming days and weeks.
"Short term, we will see the kiwi go lower, but over the next few months it will depend entirely on the path of US economic data," he said, adding that a break in the kiwi below US78c could lead to the currency falling as low as US72c.
Most of the New Zealand dollar's strength in recent years has been more about US dollar weakness, although strong commodities prices have been supportive of the kiwi.