Cruz, 19, moved in with James and Kimberly Snead of Parkland, Florida in late November after the death of his mother earlier that month from complications of pneumonia. He was a friend of their son.
Cruz killed 17 people at his former high school last Wednesday using an AR-15 rifle that he had legally purchased. It was the country's worst school massacre since the horror at Sandy Hook six years ago that left 26 dead.
In an interview on ABC's Good Morning America, Mr and Mrs Snead described their horror upon finding out that Cruz was the shooter.
"After the SWAT team called me and asked if I knew where my son Nikolas was, and I said, he's not my son, but I don't know where he's at," said Mr Snead, 48, an army veteran and military intelligence analyst.
"And at that point, I got in touch with my son, who was fleeing the scene at that point, and a description came out, and we put two and two together, me and my son, and we figured out what was happening."
Mrs Snead, 49, who is a nurse, said she was "just heartbroken" and "devastated" upon hearing the news.
"I still can't process it, what he's done because this wasn't the person that we knew," she said.
The couple said they "hurt deeply" for the victims of the shooting.
"We're devastated, and I can't imagine the pain they must be feeling, and like he said, nothing that we can say is going to be any kind of help, but we're very sorry that you know, they had this experience," she said. "It never should have happened."
The couple earlier given an interview to the South Florida Sun Sentinel newspaper.
"I told him there'd be rules and he followed every rule to the T," Mr Snead said.
"We had this monster living under our roof and we didn't know," Mrs Snead said.
"We didn't see this side of him."
A video monitor shows school shooting suspect Nikolas Cruz, center, making an appearance before Judge Kim Theresa Mollica in Broward County Court Source: AAP
A profile has emerged of a troubled young man who was expelled from the school last year for "disciplinary reasons."
The FBI admitted it received a detailed warning last month about Cruz's gun ownership, erratic behavior, and disturbing social media posts, as well as the potential of him conducting a school shooting. The agency took no action, despite the tip-off.
The Sneads described a 19-year-old who had grown up apparently without ever having to perform common chores -- he couldn't cook, do laundry, pick up after himself or even use a microwave.
"He was very naive. He wasn't dumb, just naive," James Snead told the Sun Sentinel.
Cruz had odd habits, like putting a chocolate chip cookie on a steak and cheese sandwich, and going to bed at 8 pm.
He seemed lonely and badly wanted a girlfriend, and also was depressed about the death of his mother, the couple said. Kimberly Snead had taken Cruz to the office of a therapist just five days before the shooting, and he had said he was open to therapy and took a business card.
Cruz told the Sneads he would inherit at least $800,000 from his parents, with most of the funds becoming available when he turned 22.
The couple last saw Cruz, who has been charged with 17 counts of premeditated murder, at the Broward County Sheriff's office. Dressed in a hospital gown, he was handcuffed and surrounded by deputies.
"He said he was sorry. He apologised. He looked lost, absolutely lost," said James Snead. "And that was the last time we saw him."
