In the letter, published on the website of SVT's documentary series Uppdrag Granskning, she also called for an explanation from social services in Vetlanda.
"I want to thank all of you who have shown that you care about me," she wrote, referring in particular to two women at the foster home where she currently lives.
At the end of the letter, she addressed social services in Vetlanda directly: "Why did I not get any help when I most needed it? You have said that I should have got help and that what you did was wrong. But you haven't said why," she wrote.
Social service officials in the town in southern Sweden issued a formal apology to Louise earlier this week. On Thursday, senior official Boo Hedbrant took responsibility for the council's failure to act and resigned.
The girl had been thrown out by her mother from her home in Gothenburg in 2001. Social services placed the girl with her father after visiting his apartment in Vetlanda, southern Sweden. They reported that the flat was "pleasant and light" and in a "child-friendly area."
Social services failed to note that at the time his daughter went to live with him the father was on leave from a secure psychiatric hospital, where he had been sent after being convicted of attempted murder.
What followed was years of abuse. The girl was raped hundreds of times by her father, and lived in squalid conditions at a series of homes in the county of Småland. At one point she lived in a car. She almost never went to school.
The girl's ordeal was detailed in Uppdrag Granskning. The programme, shown on Tuesday, revealed that in 2002 the girl's father took her hostage and openly threatened to kill her. Despite being informed about this and receiving several other warnings about the girl's situation, social services in Vetlanda did not intervene.
Ola Götesson, head of Vetlanda Social Services, responded to the documentary at a press conference on Wednesday afternoon:
"The criticism is justified. We have failed in our handling of this and not done our job," he said.
"I am sorry for what has happened, and would like to apologize to the girl. This is a child who has been in a bad situation over a long period," he said.
The girl escaped in 2006, and her father was arrested, prosecuted and convicted of raping his daughter. He denied the charges against him, but was found guilty and sent to a secure mental hospital. He was also ordered to pay 230,000 kronor in damages to his daughter. Vetlanda Social Services have previously been slammed by Småland County Administrative Board for their handling of the case.