In her new book Unfiltered, the Golden Globe-nominated actress writes: "Many of my deepest insecurities stem from these issues with my dad."
She also penned an open letter to the Genesis drummer, saying she forgives him for "not always being there" and "not being the dad I expected".
Collins left Lily's mother Jill Tavelman when the actress was five.
In her book of essays, Unfiltered: No Shame, No Regrets, Just Me, the 27-year-old star explains her father then moved from England to Switzerland, where he stayed for more than two decades.
"He may have still been alive, but most of the time it felt as if he were completely gone," writes Lily. "I knew he loved me, yet he wasn't physically around to tell me."
She says a "terrible disconnect" developed between her and Collins - who has four other children - as she got older.
"He assumed everything was always fine because I never said otherwise. It established a detrimental pattern.
"And I've realized that many of my deepest insecurities stem from these issues with my dad. It's taken me more than a decade to resolve some of them (others I'm still resolving) and to finally build up the courage to speak my mind to him."
The Mirror Mirror and Love, Rosie actress - nominated for a Golden Globe this year for Rules Don't Apply - encourages her readers to share an open letter she wrote with their fathers, or to write their own.
In it, she assures her father she will always need him and "always be your little girl", but also tells him: "We all make choices and, although I don't excuse some of yours, at the end of the day we can't rewrite the past. I'm learning how to accept your actions and vocalise how they made me feel.
"I accept and honour the sadness and anger I felt toward the things you did or didn't do, did or didn't give me."
She continues: "I forgive you for not always being there when I needed and for not being the dad I expected. I forgive the mistakes you made.
"And although it may seem like it's too late, it's not. There's still so much time to move forward."
Lily, whose book is published by Ebury Press on Tuesday, ends by saying: "I love you with all of my heart, more than you'll ever know."
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Lily Collins says it was "painful" that her musician father Phil was absent from much of her childhood.