The man accused of killing Karina Vetrano told cops he strangled the beautiful Queens jogger simply because he was in a bad mood, law-enforcement sources told The Post on Sunday.

“I was angry. I had some issues at home. I just lost it. When I saw her, I just hit her and kept hitting her. I hit her and choked her,’’ said unemployed Chanel Lewis, 20, according to sources.

The suspect, who was charged in the murder Sunday, told detectives that he happened to cross paths with Vetrano on a path inside Spring Creek Park while walking from his Brooklyn home to get something to eat in Howard Beach, Queens, on Aug. 2, sources said.

Lewis made “very detailed, incriminating statements” in which he described “each step of the assault,” NYPD Chief of Detectives Robert Boyce told reporters at a press conference.

Boyce added that “Karina helped us identify this person.’’

“She had the DNA under her nails, she had touch DNA on her back, and there was more DNA on the cellphone,” Boyce said, adding that the samples matched Lewis.

Lewis was ordered held without bail Sunday night at his arraignment on a second-degree murder charge in Queens Criminal Court, where he stood impassively with his wrists handcuffed behind his back.

He didn’t enter a plea or say anything, but Vetrano’s mom, Cathie Vetrano, leaped to her feet and cursed Lewis as the hearing was winding down.

“A savage murderer! He f- -king murdered my daughter, my beautiful innocent daughter! Now your nightmare begins!” she screamed.

“He’s a demon! He should be in hell and burn in hell!”

At an earlier news conference, Queens District Attorney Richard Brown said Lewis would also be charged with sexual assault.

Cops have said Vetrano, 30, was raped during the attack off a jogging path in the park.

Vetrano’s body was found with her jogging pants pulled partway down, sources have said. She put up a desperate fight against her attacker, authorities have said.

Following the attack, Lewis “had all these scratches on him, and when he went home, his mother asked him what happened and he lied to her,” a source said.

But while Lewis admitted committing the attack in “two video confessions to investigators,” he denied sexually violating the victim, sources said.

“The perp said he had a bad temper. He confessed on video about the assault specifically. He did not want to admit to the rape,” a source claimed.

Neither Mayor de Blasio nor Police Commissioner James O’Neill attended the news conference about the blockbuster arrest, which capped more than six months of investigation.

Onlookers shouted, “You murderer!” and “Shame on you!” when Lewis was led from the 107th Precinct station house — with his wrists and ankles shackled and a bulletproof vest bulging underneath a blue-and-gray striped sweater — to head to his arraignment.

He ignored questions from reporters but stared wide-eyed at news cameras and didn’t try to hide his face.

At about the same time, Vetrano’s parents spoke outside their Howard Beach home.

“It’s a good day. We can move on now,” said her father, Philip Vetrano, a retired FDNY firefighter who found his daughter’s battered body while searching with cops.

Cathie Vetrano added: “We’re glad he’s off the streets so he could never kill anyone else’s daughter. The demon must get his justice, and we will see to it.”

Her husband added, “Oh, yeah!”

Earlier, the dad left his home carrying a large club moments after Brown and Boyce formally told him Lewis had been busted.

He returned about 25 minutes later, again carrying the wooden cudgel, but wouldn’t say where he went or why.

Boyce said that Lewis does not have a criminal record but that he had received three summonses near the park, all along the stretch from Canarsie to East New York, since 2013. One was for public urination, and the other two were for violating park rules, sources said.

Lewis is unemployed and lives with his mother, Boyce said.

A man who showed up at their East New York home — a basement apartment at on Essex Street, about a mile from the Erskine Street entrance to the park — identified himself as Lewis’ father.

The man, Richard Lewis, 70, displayed a diploma showing that Chanel graduated last year from the private Martin De Porres HS in Rockaway Park, whose student body comprises “children experiencing emotional and behavioral problems,” according to its site.

The dad said he was a former principal at PS 181 in Brooklyn.

He said he first learned of Vetrano’s high-profile slaying while watching TV Sunday morning. He denied that his son was responsible.

Asked what he would say to her family, he said: “I’m sorry to hear about that, but I’m sure that he would not be a part of that.”

Richard Lewis also showed reporters a room in his apartment at the Tilden Houses in Brownsville where he said Chanel sometimes stayed.

One wall in the room was adorned with a poster of the Ten Commandments with a star-spangled border, and a pink sheet of paper with a handwritten check list that included notes reading, “6:20 a.m. watch TV,” and “6:25 a.m. wake up richard.”

“He’s a humble kid. He’s a very humble kid,” the elder Lewis said.

Additional reporting by Tina Moore, Priscilla DeGregory, Shari Logan, Kevin Sheehan and Reuven Fenton