Still, any gains will likely be muted compared with the steep falls these currencies had last year.
The poll of more than 50 foreign exchange analysts conducted this week showed the Indonesian rupiah is expected to gain the most, about 3%, followed by a 2% rise in the Taiwan dollar.
The Chinese yuan, which rose 2.9% last year, will likely gain another 1.7% in 2014 on expectations the country's central bank will widen the trading band.
"Asian markets weathered the Fed tapering announcement well at the end of 2013," said Tiina Helenius, economist at Handelsbanken.
While emerging market currencies will stay soft for some time, she expects stronger economic growth and reduced fear about the Fed's stimulus-tapering to limit the downside.
However, the poll showed Asian currencies will perform better in the second half of the year, coinciding with expectations of a pick-up in the region's economic activity.
The Fed announced in December it would reduce its monthly stimulus by $10 billion in January. Markets expect it to gradually reduce cut its asset-buying by a similar amount at each meeting - shutting the programme by the end of this year.
While that is expected to support the dollar, analysts said central banks and governments in emerging markets are better prepared to handle any outflow of money this time around.
In 2013, most emerging markets from Brazil to Turkey to India and Indonesia were caught off-guard as investors dumped assets there after the Fed signalled in May it would begin cutting bank on its $85 billion a month bond purchases.
LEADING 2013 LOSERS
The Indonesian rupiah last year led the losses with a fall of 21% against the US dollar while the Indian rupee weakened slightly more than 11%. Both countries were hurt by concerns they are highly dependent on foreign money to fund their high current account deficits.
Indonesia and India will have elections in the first half of this year and analysts said the outcomes will likely affect their currencies.
When the rupee fell at 68.85 to the dollar in August, it had "probably reached the nadir in real effective exchange rate terms," wrote analysts at BTMU in a note to clients last week on the FX outlook for 2014.
The poll showed the rupee will likely trade at 62.40 in one month, 63.00 in six months and 62.00 by December, roughly near Thursday's spot rate, on account of an improvement in the government's finances.
The South Korean won is expected to gain in the next three months but will likely lose 0.6% by the end of the year, as a weaker Japanese yen hampers prospects for Korean exports.
The Thai baht, after losing about 7% in 2013, is seen gaining some 0.8% in 2014.
While weak currencies exacerbated import costs for regional countries during a time of tepid domestic demand, analysts now expect these to help boost exports in 2014 on the back of a stronger recovery in the US
"The export-driven Asian economies are showing some response to firming global activity and stabilising Chinese growth," said Helenius of Handelsbanken.
"The developed world still matters for the region's external demand, hence the firming trend in the imports of G3 countries is a clear positive sign for Asian exports this year," she said.
