"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."
Delivering his speech partly in the Tamil language, Rajapaksa said the war was not waged against the Tamil people.
"Our intention was to save the Tamil people from the cruel grip of the LTTE. We all must now live as equals in this free country."
Minelle Fernandez, Al Jazeera's correspondent in Colombo, said: "Yesterday [Monday] we saw a lot of celebration on the streets with the announcement of the end of 25 years of war.
"There seems to be almost a sense of surprise that it has been wrapped up this quickly.
"We have been hearing reports all week that the war was drawing to a close, but seeing and hearing it is still taking time to sink in for the Sri Lankan people."
Government officials said Prabhakaran was among more than 250 fighters killed, along with his son and senior officials, as government troops captured the last piece 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."
Army officials said Prabhakaran's body had been found and positively identified on Tuesday morning.
"The good news from the war front is that the body of the leader of the terrorist organisation which destroyed the country for the last 30 years, Prabahakaran, has been found this morning by the army," General Sarath Fonseka said in an address on state radio.
He said photographs of the body would be released later in the day.
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 country, 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".
President Rajapaksa congratulated his military commanders on Monday and promised a power-sharing deal with the country's Tamil minority.
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 Tamil 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.