Eddery, an 11-time champion jockey, died on Tuesday at the age of 63.
"Filled with grief that my dad is no longer here," wrote Natasha in a post on social media.
"My sister, brother and I knew that we would lose him to his demon drink. Sadly his addiction was too strong and he couldn't overcome it."
Natasha said she was "so proud" of her father's achievements, while also revealing her pain at not having seen him for five years.
"He was an amazing jockey, father and husband, but in the end he was taken over by a terrible disease," she said.
"I don't think of that man, the alcoholic - he wasn't my dad. My dad was kind, sweet, emotional and, while he never said much, I know he loved us all very much."
Natasha, who later spoke to 5 live Sport, said it had been an "extremely hard decision" not to see her father.
She added: "We stayed in touch and spoke on the phone. I never missed a birthday, Christmas or Father's Day and not a day went by when I didn't think about him.
"The last time I saw him face to face was when I brought him home from rehab and he drank straight away.
"I turned to him and said 'dad if you choose to drink over health and family, I can't be part of that life for you'."
Natasha said it had been "so sad" to witness her father's decline in recent years.
"But that said, I loved him so much and I had probably the best childhood anyone could ask for," she added.
Eddery's remarkable riding career including 14 British Classic wins and four Prix de l'Arc de Triomphe victories.
The Irishman took out a training licence following his retirement and enjoyed further Group One success when Hearts Of Fire won the 2009 Gran Criterium in Italy.
Pat Eddery's daughter Natasha has spoken emotionally about the former jockey's "battle" with alcoholism before his death earlier this week.