DMK president M Karunanidhi said that his party's demand for an international probe into alleged war crimes stays.
"The demand we had already made stays as it is," he told reporters when asked if DMK will press for a probe against the two-time President who failed to win a successive third term.
"Both the winner and loser should think over who is responsible for the past incidents and reform," he said in an apparent reference to the ethnic issue involving Tamils.
The harshest critic of Rajapaksa, MDMK founder Vaiko, termed the former's defeat as "justice by Tamils", and took a dig at Prime Minister Narendra Modi, who had earlier wished a third term for the former Lankan President.
"International observers maintain that this election result is a nose-cut for Narendra Modi. BJP is still persisting with the man (Subramanian Swamy) who demanded Bharat Ratna for Rajapaksa," he said in a statement.
He also slammed Modi for congratulating Sirisena even before results were out and demanded that the Prime Minister should "stop his attitude of betrayal" of Lankan Tamils.
He urged Sirisena to allow entry of UN Human Rights Council investigators into his country to hold probe regarding alleged war crimes.
Vaiko said one should not expect Sirisena to deliver justice to Tamils since he had been part of the Rajapaksa government till the last minute and recalled that he had stated that he would not demilitarise Tamil-speaking areas during his election campaign.
Vaiko, however, continued his support for Eelam, a separate homeland for Tamils, saying that was the only solution to the decades-long ethnic issue.
DMDK founder Vijayakant said the victory of Sirisena was a victory of Tamils. "The new government under Sirisena should rehabilitate Tamils in their native places and restore their rights and upgrade their lives," he said.
PMK founder S Ramadoss, TMC(M) chief GK Vasan and Dravidar Kazhagam leader K Veeramani also hailed Rajapaksa's defeat. Rajapaksa had earlier conceded defeat in the bitterly fought Sri Lankan Presidential polls.
He is often criticised by Tamil Nadu political parties as he was at the helm of affairs when civilian casualties in Tamil-dominated areas in Sri Lanka's northeast reportedly peaked during the last leg of the war between Lankan army and LTTE in 2009.