The Israeli military said in February, after its own investigation into the shelling of Beit Hanoun, that it had directed artillery fire at the town after receiving reports that "militants" were planning rocket attacks.
But Tutu, a Nobel Peace laureate and UN special advisor, said his mission never had access to the Israeli report of its investigation.
"No verifiable explanation has been offered, no independent impartial and transparent investigation has been held, no one has been held to account," he said.
"This unjust and illegal action by Israel has vastly increased the suffering of a population which, being under occupation, is legally entitled to look to Israel for protection and support.
The occupation remains the root cause of incidents such as the shelling of Beit Hanoun."
Mohammad Abu-Koash, the Palestinian ambassador to the UN, said Tutu's report should be brought to the attention of both the International Court of Justice and the International Criminal Court.
"The Israeli shelling of civilians in Beit Hanoun while asleep in their homes and targeting of those fleeing is a war crime and its perpetrators must be brought before international justice."
Aharon Leshno Yaar, the Israeli ambassador to the UN, told the council: "A thorough internal investigation was conducted and the results of this investigation shared with the United Nations.
"Nothing can be gained by rehashing this topic now."
Israel and the West tightened restrictions on the Gaza Strip last year in an attempt to isolate Hamas after its fighters seized the territory, with Israel imposing a blockade.
During the fact-finding mission in May, Tutu had expressed shock at conditions in Gaza after months of Israeli sanctions.
Addressing the UN rights council on Thursday, Tutu accused the West of "silent complicity" in the Palestinian suffering and criticised the international community for failing to speak out against the suffering in Gaza, home to 1.5 million Palestinians, under the Israeli blockade.
"This silence begets complicity," he said.
|Israel said they had intelligence of militants planning a rocket attack [EPA]
"The right to life has been violated not just through the killings [in Beit Hanoun], but also through the lack of an adequate investigation of the killings.
"The right to physical and mental health has been and continues to be violated in a number of ways."
Speaking at a press conference later Tutu said: "I think the West, quite rightly, is feeling contrite, penitent, for its awful connivance with the Holocaust.
"I just hope again that ordinary citizens in the West will wake up and say 'we refuse to be part of this'."
"The penance is being paid by the Palestinians.
Tutu said that in talks with senior Hamas officials he demanded an end to the firing of rockets into Israel, saying Hamas has an obligation to respect international humanitarian law.
Al Jazeera's Barnaby Philips, reporting from the UN headquarters, says Israel was strongly condemned at the council meeting but that it was used to being isolated at such events because it believed that the council was biased against it.
He said: "Despite the international condemnation [of the Israeli blockade] there is no relief in sight for Gazans and little indication that Tutu's report can alter the grim facts of the Beit Hanoun killings."