The poll of over 25 currency strategists showed the rupee is expected to trade at 62.4 to the dollar in a month from now, 62.9 in three months and 62.0 in a year, compared with 62.2 on Thursday.
Countries with high current account deficits were hit the most when overseas investors, spooked by the Fed's hint at rolling back its massive stimulus program, pulled money out of almost all emerging markets across the globe.
The Indian rupee took one of the biggest hits between May and August, falling to new record lows before it bottomed out at 68.85, 20 percent weaker than at the start of 2013. It ended the year as one of the worst performers, down 11 percent.
The Fed last month embarked on its much awaited program to trim asset purchases, but India's government finances are less onerous now, which will keep foreigners from pulling out as much money from the country when the Fed tapers further.
"We expect a more stable year for the rupee in 2014," wrote analysts at BTMU in a note to clients.
"Net foreign institutional investor outflows are unlikely to be as large as in May-August 2013 as the U.S. Fed has made clear that tapering is not tightening, which will help contain rate expectations."
The Reserve Bank of India took decisive steps to stem the rout in the rupee last year and will be prepared to support the currency if needed.
Strategists in the poll also said the general elections due by June this year will also play a role in driving the rupee.
"We are going to face some political uncertainty over a period of time and another concern will be the reform policy measures taken after the elections," said Shakti Satapathy, analyst at AK Capital.
Prime Minister Manmohan Singh's government has been weakened by years of fractious coalition rule and has struggled to push through reforms in the labour market, taxation system and financial markets owing to lack of political consensus.
The main opposition party, led by Narendra Modi, is widely perceived by as more business-savvy and investor-friendly.