The three young kids who were critically injured when a fire tore through their Brooklyn apartment — after their dad allegedly locked them inside — still can’t breathe on their own, according to their mother.

Firefighters found the three children — Naomi, 8; Tonya, 5; and Anthony, 4 — unconscious and alone inside the 11th floor home on Livonia Avenue in Brownsville Sunday. They quickly pulled the kids out, and EMS workers labored to save them, fire officials said.

But a day later, the kids were still in bad shape.

“They are under sedation with ventilators, not breathing on their own as of yet,” their mother told WPIX outside a Manhattan hospital Monday.

“As long as they’re breathing, I am breathing,” the mom, who wasn’t identified by the outlet, said.

Authorities have charged the kids’ father, Anthony Halliburton, 37, with three counts each of child abandonment and endangering the welfare of a child for allegedly leaving them alone while he went to get groceries, according to court papers.

Halliburton, who has more than 70 previous arrests, was freed without bail Monday after his arraignment in Brooklyn Criminal Court.

He promised the judge that he wouldn’t have any contact with the kids — two of whom are his biological children.

“I am at a rage — and I will forever be upset and angry,” the mom, who was reportedly at work at the time of the blaze, told WPIX, speaking about her relationship with Halliburton. “But I have to stay calm and keep my composure, because all they have is me.”

Neighbors described a loud, chaotic scene Sunday as smoke flooded out of the blazing apartment and into the hallway.

One woman told The Post that she heard a loud banging that tricked her into thinking someone was hammering at her window.

“So I opened it, and I saw everybody looking up,” she said. “I came out, and I looked up, and I saw the fire and the smoke coming out through the windows. … It was big, black smoke covering the whole sky.”

When firefighters arrived, they found two of the kids in the living room and one laying behind the front door, John Hodgens, chief of department for the FDNY, said at a Sunday press briefing.

It’s not clear what precipitated the fire.

One neighbor told WPIX that it was ridiculous that Halliburton left the kids alone.

“There should be no reason why three kids are left in a home by themselves,” neighbor Rahnell Texsara told the station.

“His excuse to me was, ‘I was only gone for five minutes,’” Texsara said. “I’m like, anything can happen in just one minute! These are children.”

Texsara said he drenched himself in water, then tried to break into the apartment. But it was the city’s Bravest who finally breached the door and saved the kids.

Halliburton had previously been arrested mainly for the unauthorized sale of fare cards and forged tokens, law-enforcement sources told The Post.

He was also arrested twice for drug possession, sources said.

All but two of his dozens of arrests occurred in the Bronx, sources said.

One of the drug busts was in Manhattan, while a token arrest occurred in Brooklyn, sources said.