Daisy-May Brooks was hit by a car outside her home in Wolverhampton as she celebrated her sixth birthday.
In a statement her parents, Helen Brooks and Simon Davis said:
"Daisy was funny, cheeky and always happy. She would always be singing around the home.
"We are amazed at how much one little girl touched so many people's hearts.
"We don't know half the people that have been leaving flowers and mementoes outside our home.
"Daisy's death has left a gaping hole in our lives; the kids just want their little sister back.
"We would like to thank everybody for their support, family, friends all the staff at New Cross Hospital and the police officers."
Daisy leaves behind a brother, 9, and two sisters aged 11 and 8.
The 39-year-old female driver of the Honda car which hit Daisy-May stopped at the scene and was spoken to by police but not arrested.
The family says they are grateful for the support offered to them but have now asked for privacy while they grieve for their daughter.