A port spokeswoman said the firm was investigating the vandalism.
Maritime Union president Garry Parsloe said Mr Gibson was trying to distract the public. "He's losing the battle flat-out on that waterfront and he doesn't know how to control it.
"We're paying $750,000 a year to him to do what? Go around looking at billiard balls and TV sets. Rome's f***ing burning and he's worrying about a TV set?"
Mr Parsloe later called back to the Herald to say a ship due to arrive in Auckland last night and be unloaded by non-union labour was no longer heading here.
He said Mr Gibson would not see another ship in the port "unless he behaves himself" and abandoned plans to contract out the jobs of his unionised workers.
The port company later blamed a blacklisting threat from the union for a decision by the operator of the container ship Kota Permasan, carrying freight from Asia, to bypass Auckland and head to Tauranga.
It said the vessel's operator was called by a union official with a threat that it would be blacklisted if unloaded by non-strikers and the shipping company would be targeted by union action in Australia and New Zealand.
That would be illegal, the ports firm said.
Mr Gibson said "such threats, bullying and intimidation" were characteristic of the union's behaviour during the dispute and would fuel public distaste for it.
"It is abhorrent that a New Zealand union is making direct threats against shipping lines and is inciting Australians to act against the interests of our employees, Auckland businesses, Auckland City, New Zealand consumers, the New Zealand supply chain and this country."
Asked about the vandalism claims, Council of Trade Unions president Helen Kelly said she did not know anything about such behaviour, but would not condone it, and noted that the company had plenty of CCTV cameras to support an investigation.
"They are engaged in the most bullying corporate behaviour of all, and have to do something to hide that from the public, and what they have chosen to do is denigrate this workforce in many ways."