The 29-year-old's marriage to Ryan's brother Rhodri collapsed after her eight-year tryst with the footballer was exposed in June.
Natasha, who is now separated from Rhodri, has appealed for her former husband to give her a second chance, claiming that the initial "thrill" of her fling with Ryan has long gone.
"At the beginning it was thrilling to know that someone as famous and admired as Ryan wanted to be in bed with me," The Sun quotes her as saying. "But by the end the whole thing had become so seedy.
"It stopped being fun. The thrill had gone and there was nothing romantic about it. Now I sleep alone in the bed I used to share with Rhodri and wish he was back in it with me."
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Natasha continued: "I hope time can heal the pain I've caused. This has been the worst year of my life and I know I only have myself to blame for the way things turned out.
"I cheated on my husband with his own brother, who just happens to be one of the most famous men in Britain. It was never going to end any way other than badly."
Natasha also expressed regret at her "unforgivable" decision to let Rhodri discover their affair in a newspaper.
"I was such a coward. But I couldn't bear to tell Rhodri in person because it would have killed me to witness the terrible pain I'd caused him," she explained. "I knew his world was going to be blown to pieces and I didn't want to see him cry."
Natasha added: "I'm just focusing on the future. I spent my first wedding anniversary in bits. Now I'm hoping that by the time our second anniversary comes Rhodri will be back home with the children and me."
However, she added the following message on Twitter on Friday morning (December 23): "Zzzz... Rhodri and I are are FRIENDS. We will always remain FRIENDS believe what u like but #dontgetittwisted End of. Move on."
The affair went public after Ryan was revealed to have cheated on his wife Stacey with Big Brother star Imogen Thomas.
Former Miss Wales winner Thomas last week was absolved of accusations that she tried to blackmail Giggs before his identity - which had been protected by a court injunction - was revealed in the House of Commons by Liberal Democrat MP John Hemming.