The actor and comedian took his own life at his Californian home at the age of 63.
Ms Williams told NBC's Today Show there was "no point" in asking why her father killed himself.
"We don't have an explanation," she told reporter Kate Snow. "There's no point questioning it... blaming yourself or the world. It happened."
The 25-year-old said it was "going to take a lot of work to allow myself to have the sort of fun, happy life that I had, but that's important".
"Anybody who has ever lost anyone works very hard to continue that memory in a positive way."
Williams, who was famous for films such as Good Morning Vietnam, Dead Poets Society and Mrs Doubtfire, was understood to have been battling depression at the time of his death.
Hummingbird
"A lot of people feel his absence," said his daughter. "The side of him that people know and love... is the characters that he had so much fun being."
"I do think that's what a lot of people will hold on to. That's not going anywhere. They knew a dad that he was proud of them knowing. Laughter was incredibly important to him."
But she added he was also very private, calm and subdued.
Reflecting on her own memories she said: "They are mine and I love that. They are private and lovely and perhaps very different. Who knows?"
She revealed she had acquired a hummingbird tattoo on her right hand shortly after his death.
"I like hummingbirds. They're fun and flighty and strange. It's hard to keep them in one place and Dad was a bit like that," she said.
"Sometimes there are going to be days where things are really difficult and having a reminder that is permanently there is nice."
Robin Williams' daughter, Zelda, has spoken out for the first time since her father's death last August.