Elisabeth Lowe, known as Lizzie, killed herself in the Didsbury area of Manchester in September.
Lizzie was not found to have alcohol or drugs in her system, and had no diagnosable mental illnesses.
One friend told the inquest she was "finding it hard to connect with God as she thought she was lying to him".
Her father, Kevin Lowe, told the inquest: "She was just normal and seemed happy.
"There was nothing to suggest she was distressed or had any issues.
"It wouldn't have come as much surprise. She was very much a tomboy.
"In fact, she was more of a boy than some of the boys were, so it would have been no surprise at all.
"We would have been very supportive."
Mr Lowe and his wife Hilary said in a joint statement after the hearing: "Lizzie was a wonderful exuberant and loved member of her church, school and community.
"She was a gifted student, sportswoman and musician who was outgoing, fun-loving and enjoyed the love and respect of many friends.
"We are utterly devastated at losing her.
"Lizzie did not make known her struggle with depression and the challenges she tried to face alone as a young adult.
"We wish she had confided because she would have found a wealth of love and acceptance and support.
"The loss our precious daughter has left us heart broken-hearted."
Senior coroner Nigel Meadows recorded a verdict that Lizzie had killed herself.
He said: "I have absolutely no doubt they [Lizzie's parents] would have been supportive in their reaction."