Tendulkar polled 22 votes, while Naik bagged 16 in the election held at the state assembly complex today in which all the 38 state legislators voted.
The 40-member House has its current strength reduced to 38 due to resignations of two MLAs earlier. It presently has 16 Congress MLAs, 12 of the BJP, 3 each of the Goa Forward Party (GFP), the Maharashtravadi Gomantak Party (MGP) and independents and one of the NCP.
Naik was seeking the third consecutive term.
Alemao had also backed NDA's Ram Nath Kovind in the presidential election held on July 17.
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Naik was banking on the support of the like-minded parties.
All the Congress legislators voted for Naik contrary to the cross voting in the presidential poll in which at least three MLAs believed to have voted for Kovind.
"We concede the defeat. Our candidate polled 16 votes against 22 scored by the rival candidate," said Ravi Naik, the counting agent for the Congress nominee.
He attributed his victory to the BJP and its alliance partners.
"The circle is completed as the BJP now has representatives right from panchayat to the Rajya Sabha," he said.