"We expect government to do that. That is their job to find out," he said.
"[ICU] was deeply concerned and disappointed that government with all its resources was unable to receive advance intelligence that destruction and death on this scale was impending."
Furthermore, the organisation said, once the government was informed they had failed to react in a co-ordinated and effective manner or implement disaster management plans.
Pillay said the attacks were a "painful opportunity for a birth of greater involvement of civil society in protecting everyone in society".
"There is no country without a foreigner in the world", a member of the executive attending ICU's Tuesday meeting told Sapa.
Pillay said the organisation was asking their members not to retaliate or take revenge.
He said many of ICU's members were "sad, disappointed and hurt" by the attacks.
"But the majority have said they are going to build this country and they are going to stay," said Pillay.
Last Sunday, ANC president Jacob Zuma said during an address at the University of Pretoria in Mamelodi that he had heard Umshini wam was being sung during the attacks.
"That is a serious matter, for that song belongs to the ANC, it doesn't belong to unknown people. The question is who are those people who are misleading the public by singing an ANC song when they're doing the wrong thing?" he asked.
"People are abusing (an) ANC song for wrong things that they're doing and they must be condemned," he said at the time.