Human rights organizations and anti-government groups criticised Myanmar's military leaders for pushing ahead with the vote in the immediate aftermath of the cyclone.
The storm left an estimated 133,000 people dead or missing, while the UN estimates that more than one million survivors have still not received any aid.
The referendum was held on May 10, although it had to be postponed until May 24 for the areas hit hardest by Cyclone Nargis.
The government says the constitution will pave the way for a return to democratic rule with general elections in 2010, but critics say the document's provisions belie its commitment to democracy.
The constitution guarantees 25 per cent of parliamentary seats to the military and allows the president to hand over all power to the military in a state of emergency.
The generals will also have broad powers to declare states of emergency and seize direct control of the government.
The government did not allow independent observers to monitor the polling.
In a separate development on Thursday the government stepped up its criticism of opposition leader Aung San Suu Kyi's party, accusing the National League for Democracy of stoking unrest among storm survivors.
"The NLD is attempting to incite the outrage of the victims and problems, and to make the public outrage go into riots," the state-run New Light of Myanmar newspaper said in an editorial.
The NLD, which won 1990 elections but was never allowed to govern, had urged people to vote against the new constitution.
It says the constitution will only serve to entrench military rule.
On Tuesday the government announced it was extending the house arrest of Aung San Suu Kyi for another year.
The Nobel Peace prize laureate, who is barred from running for office under the new constitution, has been held in jail or under house arrest for 12 of the past 18 years.
The latest period of detention started on May 30, 2003 when she was put back under house arrest "for her own protection" after clashes between her followers and government supporters in the northern town of Depayin.