That's despite the Oly Whites' impressive showing in Japan.
Danny Hay's side beat Asian powerhouse South Korea, drew with Romania - the fourth-best European side - and were only eliminated by the host nation Japan on penalties in the quarter-final.
New Zealand finished sixth, ahead of the likes of Germany, Argentina, France and Egypt, and NZF have high hopes for 2024.
Six of this year's squad will be eligible, including All Whites Marko Stamenic and Matt Garbett and Phoenix pair Ben Waine and Ben Old, with plenty of younger talent coming through.
Adding to that, the likes of Joe Bell, Sarpreet Singh, Ryan Thomas and Chris Wood could be used as overage players.
But NZF won't be able to count on any financial assistance from HPSNZ.
"We have been told it is for senior teams and being an under-23 side at the Olympics the framework is not in place for that," NZF chief executive Andrew Pragnell told the Herald.
"It's interesting – certainly worth a discussion going forward. This is a team, although it might look different, we see on the dais at the Olympics. It's an interesting model that is operating and we have to work within the framework.
"As an observation, yes, it is an age-grade side, but does that mean that an Olympic medal is worth any less? Because that is where we see them in the future."
Since the 1992 Olympics men's football has been restricted to under-23 teams - with three overage players permitted - mainly due to FIFA's desire to avoid a clash with the World Cup.
It has still been a coveted title, with Lionel Messi (2008) and Neymar (2016) part of memorable triumphs for their nations.
But NZF didn't apply for funding for the next men's Olympic programme after being told it didn't fit the framework.
The ongoing All Whites program has also missed out despite a pivotal year ahead, with the Oceania World Cup qualifying tournament in March and the possibility of a single-leg intercontinental playoff in June, for a ticket to the 2022 FIFA World Cup.
However, NZF won't receive any financial assistance from HPSNZ for the qualification bid, due to the All Whites' world ranking (110) not being high enough.
"We were given a pretty clear steer that they were not eligible," said Pragnell. "You need to be in the top-eight medal-zone trajectory for your pinnacle events.
"That's where the model doesn't quite work, as a number of global sports and team sports are not necessarily served that well by the funding framework."
Pragnell said HPSNZ had signalled they were open to revising their frameworks and NZF were looking forward to dialogue in the new year.
"We believe that we are deserved of more investment," said Pragnell. "We have got incredibly expensive campaigns with global stars who are known by Kiwi kids [and] inspiring heroes so it certainly fits the outcome model."
On Friday HPSNZ insisted the door wasn't completely closed for men's football in the current cycle.
"We're in constant dialogue with [NZF] and we'll continue to work with them as they progress their campaign," said general manager of performance partnerships Eddie Kohlhase.
HPSNZ chief executive Raelene Castle said some sports were more dependent on government funding than others.
"Some sports have very limited capability - particularly the Olympic sports - to raise any commercial funding," said Castle. "Other sports, like rugby, football, cricket, they actually have a real opportunity to develop their own commercial support.
"So it doesn't mean the men's [football] programme is not getting any money or support. It just means they've managed to raise it through their commercial efforts."
