"We have lost a baby," the statement read.
"God takes the best too soon."
Karlissa was the youngest of five children, a beloved member of what Newman has described as a "tight-knit" family.
Touch at Mountfort Park & Gallaher Park have both been cancelled tonight, in respect of the tragic accident that...
Posted by Counties Manukau Touch on Thursday, 13 December 2018
Her parents said the remaining children were "very sad".
"Karlissa was our baby girl."
In light of what they're going through, Jen and Dan urged people to show kindness and love to one another.
"Our request is that people love their whānau at this time," they said.
"It is Christmas time."
The family also thanked the wider community for rallying together in support.
"Tears are a reflection of love... An ocean of love is being expressed at this time."
The extended family was helping out with plans moving forward, focusing particularly on supporting the remaining four children.
Speaking to the Herald this morning, Daniel Newman said the family had only moved into the Papakura home three weeks ago, and "didn't have much to come and go on".
They were facing big costs for the funeral, he said.
"There is no reference for this kind of thing - we're right on Christmas and they are a family who are quite tight knit."
"It doesn't get much worse than that."
The incident occurred on the park's number two field, Newman said, which less than a week ago had hosted thousands of locals for the Manurewa Christmas in the Park.
A Givealittle page has been set up by a friend of Karlissa's parents, aiming to ease the financial burden faced by family as they "send off their precious beautiful baby".
Victim Support was assisting the family of the deceased, who were present at the time of the incident.
Police had extended their "heartfelt condolences" to the family.
