Police were following the man after he left home and walked into the New Lynn Countdown this afternoon, before he took a knife from a shelf, and carried out the attack.
Three of the six shoppers are in a critical condition in hospital.
Police are now investigating the attack and Coster tonight called for any witnesses or those with photos or video of today's incident to assist by submitting them to officers on 105 quoting Operation Rally.
An online portal has been set up and people can access this at https://rally.nzpolice.org.
In a statement, Coster said the man had been under police surveillance "because of concerns about his violent, extremist views".
Covert Police Specialist Tactics Group operators had been watching the man "as closely as possible without detection" and responded within about 60 seconds of the attack beginning, he said.
"The police staff challenged the man and diverted his attention. He charged at them with the knife and the officers shot him," Coster said.
He died at the scene shortly afterwards.
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Police are not seeking anyone else in relation to this attack as they are confident the man acted alone.
Three people suffered critical injuries and were taken to Auckland City Hospital.
A fourth person is in a serious condition, and a fifth was taken to hospital in a moderate condition.
A sixth victim made their own way to Waitakere Hospital after the incident with moderate injuries.
"The attacker was under constant surveillance and was today observed leaving his Glen Eden property and travelling to the supermarket, as he had done previously without incident," Coster said.
"Our police staff acted quickly and with great courage to stop this man and prevent any further harm to members of the public."
Coster also praised members of the public who helped out at the scene and sympathised with victims.
"Our thoughts are with the victims of today's attack, their families and those who were caught up in this horrific event," he said.
"People have an absolute right to feel safe going about their normal activities."
The scene is currently locked down and will be the subject of an extensive scene examination.
Police are also in the process of compiling witness information and collecting CCTV footage.
Officers will continue to have a high presence in the area by conducting patrols over the coming period.
"We want to assure the community that these were the actions of a lone individual with a violent extremist ideology," Coster said.
"He did not represent any New Zealand community and responsibility must lie with him alone."
Police will also ensure support is available to anyone affected by today's event, he said.
