"Our container operations at Fergusson Terminal are not affected by this decision and continue to thrive. Over the coming months we expect to be able to announce a number of exciting new initiatives to improve that part of our business further," he added.
The Auckland Council has also decided not to appeal the decision.
It has commissioned a Future Port Study to look at the wider effects of the port on the city.
Last week, High Court Judge Geoffrey Venning ruled in favour of Urban Auckland - a society of architects and planning professionals - which challenged the lawfulness of the consents for the extensions.
The consents were granted late last year by Auckland Council.
Justice Venning ruled the consents should not have been granted for the project without the public first having a say.
The port has stopped work on a $22 million contract to build the extensions.