It was the worst holiday weekend imaginable for some new Hamptons eateries — they couldn’t snag liquor licenses in time, leaving their tony customers, gulp, without booze.

“People work hard. They come out here, and they want to have fun,’’ said Zach Erdem, who brought in Michelin-star chef Terrance Brennan to run his new Southampton restaurant, Blue Mar.

“They are ordering beautiful pieces of fish from a top chef, and they can’t eat without a nice glass of wine.”

TBar in Southampton decided not to open at all because it didn’t get its license.

“It would have been too stressful,’’ said co-owner Tony Fortuna, who had planned to open Thursday.

He estimated that he and his partner lost about $125,000 by staying shuttered over the Memorial Day weekend. They are hoping to open around this Thursday.

The situation was not just upsetting to the owners or customers, either.

Erdem said he lost half his workers by Sunday — because slinging drinks is where the most tips are made.

“I woke up this morning to find out that [many of] my staff have already quit: six bartenders, three servers, two managers and four cooks,” Erdem lamented. “I’ve lost so much money. I don’t know how long I can stay open while I wait for the license.’’

Blue Mar and others offered free wine in a bid to appease their booze-thirsty diners, but Erdem said a lot of his customers still canceled their reservations over the snafu.

It was only a couple of months ago that the foodie businessmen thought they’d hit the jackpot.

Rents had been soaring so high in the Hamptons that many eateries started to go empty, prompting the savvy restaurateurs to scoop up the coveted spots at highly discounted prices during an 11-day frenzy in April.

Stefano Marracino of Paola’s East had been dreaming of opening a Hamptons outpost of his popular Upper East Side spot, Paola’s, for six years and finally signed a local lease in April.

But several weeks wasn’t enough time for local municipalities to process his and the other new establishments’ liquor-license applications by the holiday.

The [owners] worked so hard to open fast, and now they are just waiting,” said Don Evans, who works with top chefs to produce food events in the Hamptons and New York City.

Marracino told The Post that he hopes to get his liquor license this week.

Erdem said he applied for his license April 26 and, “My check was cashed.

“So why can’t anyone tell me when I’ll get the license or if I’ll ever get it? It doesn’t make sense,’’ the restaurateur said.

“If you don’t give me my license on my busiest day of the year, when will you give it to me? At the end of September?’’ he asked, adding that he paid $450,000 in annual rent in the hopes of making it up — and raking in much more — in the crucial three summer months.

“It’s not right,’’ Erdem said. “I have a great chef. But he’s not happy. No one is.”

Fortuna said he tried to make the best of the bad situation by using the extra time to prepare for an even better opening.

“Everyone who opened without their licenses had issues. Besides, were we really ready to open? Not really. So … it actually helped us out,” he said.

The weekend wasn’t all bad for Erdem, either.

His other Hamptons restaurant, 75 Main, which is across the street from Blue Mar, never did better, he said — likely because he offered customers headed to his new joint an established boozy alternative.

“We had 850 dinners last night and 700 lunches. There were long lines and people were trying to sneak in the back entrance. It was crazy,” Erdem said.

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