Mrs Longstone said the system needed to be more equitable for New Zealand to stake a claim to being a world leading education system.
"In order to be truly world class we need to be both high performing and high equity.
"The first step to dealing with an issue is to recognise it," she said on Radio New Zealand.
New Zealand Education Institute (NZEI) national secretary Paul Goulter said Mrs Longstone's comments put her at odds with Ms Parata, who last week released a statement saying New Zealand's education system was among the best in the world.
He questioned why Mrs Longstone would make her comments when students continued to outperform most other countries.
"Is this part of a real agenda to undermine and discredit our public education system in order to bring in radical, experimental and failed overseas policies, such as dodgy charter schools using unregistered and unqualified teachers?" Mr Goulter said.
The education system was making progress for vulnerable groups, which was shown through the increase in the number of Maori and Pasifika children gaining NCEA qualifications, he said.
NZEI President Ian Leckie said Mrs Longstone had gone too far with her comments.
"To say that New Zealand's education system isn't world class is absolute misinformation and I'm surprised to see that actually stated in writing."
He said New Zealand was still up there with the best in the world.
Among OECD countries, 15-year-olds in New Zealand were ranked fourth in literacy and science, and sixth in maths.
In the same OECD studies, New Zealand ranks lower in terms of equity and diversity.
