Last week, an inquiry found New South Wales health authorities made "serious mistakes" in allowing about 2,650 passengers to disembark when the ship docked in Sydney in March.
Those people were not tested for the virus, despite suspected cases aboard.
The ship was ultimately linked to at least 900 infections and 28 deaths.
Prior to Australia's second wave of the virus - which emerged in Melbourne in June - the cruise ship had been the source of Australia's biggest coronavirus cluster.
NSW Premier Gladys Berejiklian said she was particularly sorry to the 62 people who had caught the virus from passengers who disembarked.
"I can't imagine what it would be like having a loved one - or being someone yourself who continues to suffer and experience trauma as a result - and I want to apologise unreservedly," she said.