He said health was important but so was ensuring the livelihood of people and businesses.
"Lockdown ... it is the last thing you turn to."
Goff hoped health authorities were prepared for a rise in tests but urged the public to only get tested if they were symptomatic or had been in the same locations as the positive cases.
"Don't get tested if you don't need to be tested."
He said Auckland was more vulnerable to an outbreak because its airport was where most international returnees arrived and also where there were the most number of managed isolation facilities.
"That's a burden we carry for the rest of the country."
The three positive cases from the Pullman suggested some "systemic failure" and there was a need to get to the bottom of it, he said.
While New Zealand had been largely able to contain the virus, "we are not failsafe", he said.
As for the upcoming long weekends of Auckland Anniversary and Waitangi Day, he said there was no word yet from public health authorities to stay home. "At this point it not deemed necessary."