The storm has reportedly lessened slightly as it headed northwest on Sunday, reported BBC News.
CNN on Sunday said it had become a Category 1 hurricane — hurricanes are called cyclones in the Indian Ocean — dropping down from a Category 4.
It was at that strength, packing 140-mile-an-hour winds, that the cyclone made landfall Saturday in Odisha state.
A top disaster management official told Agence France-Presse that 14 had been reported dead, far less than initially feared.
"We have been able to... (keep) the death toll to a bare minimum," vice chairman of the National Disaster Management Authority Marri Shashidhar Reddy told reporters in New Delhi, AFP said.
The worst storm to strike India in 14 years, Phailin tore through coastal homes in India's southern Odisha and Andhra Pradesh states on Saturday.
According to India's Economic Times, the powerful cyclone also sunk a cargo ship carrying 8,000 tons of iron ore.
"The Panama-registered cargo ship MV Bingo is feared sunk as the crew was sighted on a lifeboat yesterday east of Sagar, 25km from the coast," Kolkata Port Trust head Kahlon said on Sunday, reported the Times.
Disaster relied officials and residents on Sunday worked to clear roads and assess the damage.
Watch India's NDTV report from Ganjam, the area hardest-hit by the storm, here: