"The Sri Lankan government may have declared a military victory. But it does not realise that it is a hollow victory. It has completely lost the trust and confidence of the Tamils in Sri Lanka," he told the pro-LTTE website Tamilnet on Monday.
"Our struggle will continue until the aspirations of our people are realised," he added.
Government officials said Prabhakaran was among more than 250 fighters killed, along with his son and senior officials, as government troops captured the last sliver of territory held by the separatist group.
"Over 250 dead bodies of terrorists are scattered over the last ditch," Lieutenant-General Sarath Fonseka, the head of the Sri Lankan army, said in a statement.
"All military operations have come to a stop. Now the entire country is declared rid of terrorism."
Military sources said Prabhakaran's body was found in an ambulance destroyed by troops as it sped out of the war zone.
|The army says it has killed Prabhakaran but the LTTE denies it [AFP]
Officials said that Prabhakaran's corpse had been badly burned and DNA tests and other tests would be carried out on the body, but Chamari Danansuriya, a magistrate, described the process as a legal formality.
The Tamil Tigers had been striving to carve out a separate homeland for ethnic Tamils in the country's north and east. They accused the Sinhalese-dominated government in Colombo of neglecting Tamils.
The group once controlled nearly a fifth of the Indian ocean island nation, running a shadow state that had courts, police and a tax system along with an army, navy and even nascent air force.
But on Sunday, it said it would "silence [its] guns", declaring that its battle with the government had come to a "bitter end".
Reports of Prabhakaran's death sparked celebrations in the capital, Colombo, and the president congratulated his military commanders on Monday.
Rajapaksa has promised a power-sharing deal with the country's Tamil minority.
But the government faces scepticism that it will be genuinely inclusive now that it has defeated the LTTE.
It also faces a looming humanitarian crisis with the UN estimating that 8,000 people were killed and about 250,000 displaced in just the last four months of the conflict.
The government and the Tigers alike were criticised for not allowing civilians to leave the conflict zone and firing on them.
UN officials say Ban Ki-moon, the secretary-general, is expected to visit Sri Lanka this week, where he will focus on trying to help the displaced, pressing for their speedy return home.