In a blog post published on Wednesday, 30-year-old writer and actress Rosa listed '11 life lessons from my Dad'.
"My darling Dad has died," Rosa began the post. "I loved him to the ends of the earth and he loved me back just the same.
"These are the lessons he taught me, I will keep them close to my heart and remind myself of them whenever I stumble or falter," she added. "They are his words; the words spoken so often to encourage, comfort and reassure. This isn’t general wisdom, rather advice that he tailor-made just for me. I love you Dad."
Bob's advice includes telling Rosa, whose mother is the actor's second wife Linda Banwell, to 'laugh', 'be yourself' and 'don't worry about other people's opinions'.
Rosa and Bob Hoskins
"What ever you do, always give it a good go," she recalls him teaching her. "Don’t be afraid of failure and disappointment. If you fall flat on your face then get straight back up. You’ll always regret not trying. Disappointment is temporary, regret is forever.
"Get angry, it’s ok to lose your temper now and then," reads another item on the list. "If anger stays in, it turns to poison and makes you bitter and sad. Get angry, say your peace, then let it go."
Linda Banwell and Bob Hoskins with their daughter Rosa
North London-based Rosa also remembers her father teaching her to 'be kind', 'make memories' and 'never, ever, ever, ever give up.'
"Love with all your heart," Rosa concludes the list. "In the end, love is the only thing that matters."
The sad news came less than two years after the star of Who Framed Roger Rabbit announced his retirement from acting after being diagnosed with Parkinson's disease.
At the time, his agent said that after a "wonderful career" spanning four decades, the star was withdrawing from acting to spend time with his family.
"He wishes to thank all the great and brilliant people he has worked with over the years, and all of his fans who have supported him during a wonderful career," read the August 2012 statement.