About 50 council staff, most of whom had recently returned from overseas, were in self-isolation, he said.
"What is happening at present is unprecedented in our lifetime, and the fast-moving situation means we need to be ready to constantly lift the level of our response," Goff said.
He said the Ministry of Health is the lead agency and council is acting on and not reinterpreting their advice.
"We have responded rapidly to cancel major events and are ready to take further action should that be necessary."
Goff said revenue losses in some cases will be quite significant, saying Ports of Auckland had already signalled a sharp drop in its dividend due to an investment programme and Auckland Airport has suspended a dividend of about $60m. Revenue could also be down from fewer people using public transport.
He said that was going to place constraints on council spending in the upcoming July budget where there will be limited room for new spending and desirable, but non-essential items, could be deferred.
This is the new world we are operating in, said Goff, saying people have got to lower their expectations because there won't be any spare money.
Asked about assistance for people who still struggle to pay rates, Goff said council officers are looking into that.
The Government, he said, could borrow to pay for its $12.1 billion assistance package, but the council - which is at the upper limit of its borrowing without risking a credit downgrade - could not borrow to fund a relief or recovery package.
"We are looking pretty much at the Government which has got the room to manoeuvre in that area," he said.
Goff said he did not see public transport being closed down unless council gets very strong advice to the contrary, saying even Paris, in lockdown, is keeping its metro system running.
The mayor's message of Aucklanders is panic is never a great reaction to any crisis.
"We are facing a health and potentially an economic crisis. Listen to what health authorities are saying. On the economic front just be aware these things have cycles and that cycle will come to an end."
In the meantime, he said, Aucklanders should follow the government's advice: be kind, wash your hands regularly and stay up to date with official updates.
"The new government website at covid19.govt.nz is a useful resource with all the relevant information in one place."
Cancelled events include:
Music in Parks
Fri 20 Mar – Music and Food – Te Atatū Peninsula
Sat 21 Mar – A Little Bit of Everything - Hobsonville Point Park
Sun 22 Mar – Brass at the Falls – Falls Park, Henderson
Sun 29 Mar – Love Songs from the Underground – Auckland Domain
Sun 29 Mar - Brass at the Falls – Falls Park, Henderson
Sat 11 Apr - Party in the Park – Maybury Reserve, Glen Innes
Movies in Parks
Fri 20 March – The Secret Life of Pets 2 – Milford Reserve, Milford
Sat 21 March – Toy Story 4 – Fergusson Domain, Oranga
Fri 27 March – Spider-Man: Far from Home – Rosedale Park, Albany
Sat 28 Mar – Abominable – Murphy Park, Ōtāhuhu
Fri 03 Apr – Poi E – Coyle Park, Pt Chevalier
Sat 04 Apr – MIB: International – Te Puru Park, Beachlands
Thu 09 Apr – E.T. the Extra-Terrestrial – Woodall Park, Narrow Neck
Sat 11 Apr – Daffodils – Waiake Reserve, Waiake
Fri 17 Apr – Dumbo – Luckens Reserve, West Harbour
Sat 18 Apr – Season Finale – Brains Park, Kelston
