Auckland's descent into a fourth lockdown showed New Zealand was losing its lustre as a global leader in the fight against coronavirus, Seymour said.
A 21-year-old man who went to a gym after getting a Covid test, before receiving a test result, has caused widespread frustration in South Auckland and beyond.
Seymour said people might have strong instincts for retribution against those seen to have endangered the community.
But he said calls to harshly punish those who breached Covid protocols could lead to people being penalised for innocent mistakes.
He said Taiwan's success stemmed largely from lessons learned and investments made after the early 2000s Sars pandemic.
National Party leader Judith Collins told TVNZ's Q+A police should be dispatched if people in isolation did not respond to Government messages within 24 hours.
Under the Health Act, police may use force to ensure compliance with a medical officer of health's requirements, such as self-isolation.
Prime Minister Jacinda Ardern said police would join health authorities if it was suspected people were not self-isolating.
She told a press conference today most people did already respond to messages and checked in when required during self-isolation.
"What we have here are a handful of cases where they haven't, and it has had dire consequences.
"What we will be doing is enabling health of course to work with police when they have concerns that someone is not following the rules, to have a check-in in place.
"We try to leave as little excuse as possible for not hearing the message that we are at level 3 in Auckland," Ardern added.
She said despite the country's efforts, some recent cases had gone to work when they should not have.
"When you get a test, you must isolate at home until you've received a negative test result," Ardern said.
She said financial support was available during the pandemic, including the Short-Term Absence Payment for people unable to work while waiting for test results.
Ardern and Health Minister Chris Hipkins both expressed annoyance at the latest case but urged against demonising the man known as Case M.
The new South Auckland cases led community leaders there to voice irritation, but to also call for unity.
Case M spent four hours working as a casual contractor at Kerry Logistics Oceania in South Auckland early last week.
Kerry Logistics managing director Rob Gilhooly said the case was frustrating.
"We've taken all the precautions. The facility has been deep-cleaned today."
He said Case M arrived on site through an external labour hire company.
The labour company said the man visited Kerry Logistics on Tuesday, and details of Case M's contacts were supplied to the Ministry of Health as requested.