Curacao might be mistaken for a fancy tropical drink, but the Caribbean team are the real deal, ranked No 79 in the world by Fifa (New Zealand are 121).
This was their eighth game in 2021, and they have some outstanding players, led by Juninho Bacuna (Glasgow Rangers) and Leandro Bacuna (Cardiff City).
But they were outplayed and out hustled by a hungry All Whites team, who were good value for the victory, in challenging conditions and 32 degree heat.
"It's fantastic for the players," said Hay. "[In] difficult conditions against a top 80 side, so a good win.
"It's quite nice to come off a bit disappointed, we should have wrapped the game up much earlier but there will be some good lessons for the young players, the fact we had to grind it out and get the result."
The result sets things up well for the clash with Bahrain on Wednesday (5am). They beat Curacao 4-0 last week, though the scoreline flattered the Asian team.
The All Whites will be without Sarpreet Singh, with the midfielder returning to his club, Jahn Regensburg, in Germany's second tier. Singh was a standout on Sunday, with reminders of his poise and skill in possession.
"He showed his class and a lot of the game plan was trying to get him on the ball," said Hay. "He is an incredibly intelligent player and one that we really need to look after and nurture.
"We are aware that he is in a critical period of his professional career and needs to cement himself fully in the German game."
Chris Wood is expected to be available, after getting through Sunday's game.
Carrying a slight knee injury, Wood couldn't train leading into the match, but an MRI scan concluded there was minimal chance of further damage.
"He was determined to play," said Hay. "We supported that and he got through it."
Aside from the first half goals to Bill Tuiloma and Wood, New Zealand created numerous opportunities, but couldn't apply the final touch or accurate pass.
"It's a good learning for a young group that we need to be more clinical in those periods or you allow teams to get back into the game," said Hay.
"We showed real courage on a pitch that wasn't fantastic to play on and in pretty trying conditions. We ran out of steam a little bit towards the end, because we did try and press for long periods of the game."
Tuiloma smashed home a ninth minute free kick – via a helpful deflection off the defensive wall – while Wood make no mistake with his left foot finish in the 33rd minute, after Marko Stamenic had won possession, with Callum McCowatt supplying the cross.
It was reward for a strong start, as New Zealand pressed and harried, not allowing their opponents time on the ball.
The midfield quartet featured the uncapped Stamenic and Matthew Garbett (both 19), along with Joe Bell (22) and Singh (21). They linked well with McCowatt and Wood, while Liberato Cacace was a constant threat on the left flank.
It wasn't easy on the spongy surface, but there was some intricate work in possession.
Niko Kirwan had a solid debut – aside from an unfortunate error that contributed to Curacao's 72nd minute goal to Rangelo Janga – while Nando Pijnaker andTuiloma were mostly assured at the back, with Tommy Smith, Michael Boxall and rookie Kelvin Kalua having late cameos.
Goalkeeper Stefan Marinovic made a couple of fine stops, highlighted by a late one on one save to deny Janga.
Marinovic has drifted off the radar for local football followers, after being usurped by Oli Sail at the Phoenix, but the long-time New Zealand No 1 showed his value and experience on the international scene.
Tuiloma (hip flexor) may be in doubt for Wednesday's game, though Boxall should be recovered from an illness that prevented him starting on Sunday.