The EastEnders actor, who plays Ryan Malloy in the BBC One soap, issued an apology to his wife and family for sleeping with the teenager.
Speaking to the Sunday Mirror, he said: "I am so sorry to my wife, daughter and our family for this betrayal. I love my wife and family dearly and I'm distraught that my life is now in tatters due to a stupid mistake.
"I've no excuse for my actions but I had no idea the girl wasn't over 18 as we met in a nightclub. Either way, I've caused heartache to those I love most which I deeply regret.
"This was a one-off incident but I've let myself down as well as my wife and everyone who knows me. Now I just need privacy and time to do all I can to rebuild my family."
McDermott met the girl at Glam nightclub in Stockton-on-Tees last Saturday while signing autographs and playing a Blind Date-style game.
The girl told a friend: "Ryan just started staring at me through the crowd. It was so obvious that another girl, who I didn't even know, turned to me and said, 'he keeps looking at you'."
When the student paid the £5 to go on stage and have her photo taken with him, McDermott took the opportunity to get to know her better.
She said to her friend: "I was a bit starstruck to be honest as I love EastEnders and I've always really fancied Neil's character Ryan.
"I was very drunk, but he was really nice and friendly and not sleazy at all. He just kept smiling at me. At one point he started telling me about his wife and baby.
"As I was leaving the stage, he said he was going to the Parkmore Hotel and that I had to leave with his people. I remember he kept repeating, 'the Parkmore, the Parkmore'."
When the girl arrived at the hotel, McDermott was waiting at the bar and told her to pretend she was his cousin. Not long after he invited her back to his room.
The friend added: "She immediately said yes. Even though she'd only just met him she said it seemed as though they'd known each other for years. He was really lovely and she really fancied him."
After talking for a while, he told her that he was "going to bed" and they had sex.
The next morning McDermott got up early to return to his family in Surrey.
The girl's friend said: "She asked him if he felt bad about having sex with her. He said, 'It's been done now', which seemed a bit cold. But then he said "I've never done this before' and she has told me she believed him.
"At that point she said he seemed really sad so she asked him what was the matter. He didn't answer, instead he just looked away and carried on getting his stuff together."
When he was leaving he told the girl: "Good luck, see you later." They did not swap numbers and have not had contact since.
McDermott met his wife Michelle at London's Mountview Academy of Theatre Arts when he was 19 and she was 18. They have been together ever since, and married at Airth Castle in Scotland in 2007.