He said "it doesn't mean that the cells and organisations that work and move in Indonesia and in Southeast Asia have been crippled".
Yudhoyono said that in the future "we have to save our country, our people, our community and our young generation from the temptation to involve themselves in terrorism and save everything from terrorism".
Kevin Rudd, the Australian prime minister, congratulated Indonesian security forces for their "success" but echoed Yudhoyono's warning.
"It doesn't leave us in a position where we can feel complacent about the future. Jemaah Islamiyah is still alive and well. Al-Qaeda is still alive and well," he told the Australian Broadcasting Corporation on Friday.
Yudhoyono said nations across the world needed to address injustice to eliminate acts of terror.
"There is a perception, a feeling; that the world looks unfair, that the rich are getting richer and the poor are getting poor ... the wars in the Middle East, in Afghanistan, Iraq, Palestine and many other global problems are seen as a result of global injustice," the Jakarta Post quoted him as saying.
Pointing to poverty and underdevelopment along with radical and extremist beliefs as root issues, Yudhoyono said "the solution is we have to build a just, peaceful and prosperous world".
John Harrison, an expert on terrorism at the Institute of Defence and Strategic Studies in Singapore, told Al Jazeera that it may not be so easy to replace Noordin because "there are very few individuals that combine the charisma, the organisational abilities plus the connections that he had".
But he cautioned that Jemaah Islamiyah (JI), the group Noordin was linked to, is "always able to replace individuals".
Harrison explained that JI had been relatively quiet in the past few years partly because of reduced capacity due to many members being killed or arrested, and because it was "in a strategic discussion to determine whether or not they can use violence and … how to do it without killing large numbers of Indonesians".
But he cautioned that "JI should not be underestimated - they are a militant group that wants to use violence.
"Until the ideology that is fusing and infusing this movement is addressed more comprehensively, they will be able to replace their losses that will happen from time to time.
"Many young males ... have been very angry, they've been frustrated, there have been a whole series of reasons that they have decided to be attracted to and perhaps engage in violent activity.
"And until the political aspects of that, that bring together these frustrated individuals, give them a reason for committing violence, and a justification for that, is addressed, we will continue to face these waves of violence and sometimes very extreme violence for years to come.
"There needs to be a much more comprehensive strategy for addressing those types of issues."
Indonesia's national police chief said fingerprints taken from one of four bodies removed from the house following the raid matched those of Noordin's.
The bodies were flown to Jakarta for autopsies and DNA tests.
|Police said fingerprints taken from one of the bodies on Thursday matched Noordin's [EPA]
Counterterrorism troops sealed off the area near the house in a suburb of Solo city late on Wednesday, searching for suspects involved in the July 17 attacks on the Ritz-Carlton and JW Marriott hotels in Jakarta which left nine people dead and 53 wounded.
Documents and laptop computers indicating that Noordin was al-Qaeda's leader in Southeast Asia and hundreds of kilograms of explosives, M-16 assault rifles, grenades and bombs were recovered from the house, police said.
Noordin is believed to have headed a splinter group with connections to Jemaah Islamiyah, a group fighting for an Islamic state in Southeast Asia.
In a 2005 video, he claimed to be al-Qaeda's representative in Southeast Asia and to be carrying out attacks on Western civilians to avenge Muslim deaths in Afghanistan.
He was also wanted in connection with the Bali bombings in 2002, which killed more than 200 people, and a number of other deadly attacks.