The Government says Bermuda is a "much less attractive" choice as an America's host because of the scarce opportunities to promote New Zealand business there.
The island off the east coast of the United States was this morning chosen over San Diego to host the 2017 event.
Team New Zealand is seeking further taxpayer funding for its next bid, on top of an initial $5 million investment.
Economic Development Minister Steven Joyce said he expected to receive a funding proposal from the syndicate quickly, but he was not excited by the prospect of investing public money in the Bermuda event.
"My view is, get a proposal on the table, we'll have a look at it. But I've been pretty clear that Bermuda is much less attractive from the New Zealand Government's perspective in terms of what we can do to promote New Zealand."
In comparison, the previous campaign in San Francisco provided numerous opportunities for New Zealand's food, beverage, IT, and high-tech manufacturing industries to get leverage into a crucial market.
"Bermuda is ... in the ocean in the middle between the US and Europe, less attractive for us, mighty fine for other sponsors but I've checked with our agencies and they're less excited."
Government invested $36 million in the 2013 event and Team New Zealand was likely to seek a similar amount again.
Mr Joyce said there could be a consolation if Auckland was given hosting rights for one of the qualifying rounds for the America's Cup.
But Team New Zealand would have to consult other syndicates over the possibility of a challenger series in Auckland, which could take some time.
"Which is frustrating for us frankly and, I imagine, also for Team New Zealand," Mr Joyce said.
He said details about a challenger series in Auckland were "a bit sketchy at the moment".
Labour: Bermuda has some benefits
Labour's sport and recreation spokesman, Trevor Mallard, who signed off on funding for Team New Zealand's 2013 bid, said there were some advantages in having Bermuda host the event.
It had a favourable time zone, which meant the New Zealand brand would be broadcast in the US, Europe and the Middle East.
Mr Mallard said the high-profile yachting event always attracted "high net worth" individuals and prospective investors, and Bermuda would be no different.
On the downside, Bermuda was not a gateway to the high-tech industry like San Francisco, where the last cup event was held.
It was more difficult to access from New Zealand. This meant it would be harder to justify the sort of on-the-ground leverage work that took place in San Francisco, such as hosting large networking meetings for New Zealand companies.
Bermuda's remoteness also meant Team New Zealand's transport sponsors, Maersk and Emirates, would have to make a bigger commitment if they backed New Zealand's bid again.
Mr Mallard said the Government could still benefit from the event, regardless of the venue, if the boat-building and design work was based in New Zealand.