The girl is recovering at home following the incident at Rangiora's Good Street Reserve on Sunday afternoon.
Francesca Laffey said daughter, Chloe, was "definitely a tough little thing, a wee battler".
Chloe was at the park with her grandmother when a dog attacked her.
"She was playing on the flying fox when the dog jumped up and bit her," her mother said.
The dog's owners were at the park when the incident happened.
Francesca Laffey said it was too soon to know what effect the incident would have on her daughter's confidence around dogs.
"There will probably be some effects I'm sure, but as I say she is a tough wee thing so hopefully she bounces back and doesn't let it affect her too much."
Waimakariri District Council spokesman Matt McIlraith said the dog, an American Bulldog / Pit Bull mix, was euthanized on Monday night.
Laffey said that was a relief to her and the family.
"We are animal lovers, but if a dog is capable of doing something like this then there is always the chance it could do it again and I would hate for another family to go through this."
Laffey said Chloe had asked her questions about the attack, including why it happened.
"She has told me she wished she had never gone to the park.
"We've just told her it wasn't her fault at all and that she should never have to worry about going to the park and playing."
Laffey urged dog owners to keep their animals off playgrounds.
"You would hope that dogs would not be off leads and on children's playgrounds; there is too much opportunity for them to get over-excited and things can happen.
"I would also urge parents who are concerned about dogs in playgrounds to have the courage to approach the owners and tell them."
McIlraith said the council implored dog owners to look after their pets in public spaces and keep them under control.
"This is particularly relevant with summer on us as pets and their owners are out in force in public places around the district, making the most of the great weather."
Chloe would be off school for a while, but was "still perky", her mother said. "I've had to remind her not do things and take it easy."
The council was still investigating the attack and was yet to decide whether it would prosecute the dog's owners.
(Stuff NZ - November 29 2017)