"Schools will be forced to make trade-offs between the critically important work support staff do and meeting rising operating costs."
The operations grant covers costs from support staff salaries to toilet paper and electricity bills.
Merivale School principal Jan Tinetti said what was being called targeted funding to better serve those in need amounted to little more than "rearranging deckchairs".
"As I keep saying, our system overall is inadequately resourced. A funding freeze amounts to schools and children missing out across the system.
"Operational costs are continually increasing and without the funding increase schools will have to trade off other areas to pay these costs."
Ms Tinetti said one of the only areas where schools had flexibility over funding was support staff
"Personally, I find this heartbreaking when I have to make impossible decisions over the essential human resource and operational costs."
Ministry of Education Deputy Secretary Ellen MacGregor-Reid said NZEI's claims that there had been a funding cut for schools in 2016 were based on a flawed analysis and all schools would receive additional funding per child this year.
"The NZEI claims around the 0.5 percent per-student funding reduction in 2016 are based on an Infometrics report it commissioned. The report suggests the reduction has occurred in the 2016 year as a result of roll growth," Ms MacGregor-Reid said.
"The Ministry of Education has discussed the report with Infometrics and explained that their conclusion is not possible and that the assumptions they have used are wrong.
Ms MacGregor-Reid said for the 2016 school year, all schools benefited from a one per cent increase in the operational grant funding rates. Inflation was steady at 0.4 per cent, so schools would still benefit from extra funding once this is taken into account.
"Additional factors determine the total value of operational funding schools finally receive, including the size of the roll. If a school's roll increases, the amount of operational funding paid to each school increases accordingly."
Ms MacGregor-Reid said an extra one per cent was also provided in Budget 2016 for the 2017 calendar year, which was targeted to 150,000 students identified as being most at risk of educational under-achievement.
"The exact number of schools who will receive the additional targeted funding will be announced in September. However we estimate about 98 percent of schools will get funding through the targeted approach. This therefore is not a funding freeze, as NZEI has claimed."
