Steenkamp's death has left a void, says family
"There is a space now in the family. We will miss her words," he said in a short statement. He had earlier delivered a eulogy at the funeral.
He said the family would try to maintain the positive attitude towards life which Reeva had embodied.
Her uncle Mike Steenkamp thanked the media for honouring his niece's memory through its coverage of her funeral.
"Like the pastor said, we will keep Reeva in our hearts forever."
He thanked those in South Africa and abroad who had sent the family messages of support.
"The compassion people have shown was tremendous," he said.
Steenkamp was shot dead on Thursday at the home of her paralympian boyfriend Oscar Pistorius.
Mike Steenkamp said the family appreciated the media keeping their distance at the funeral so they could say goodbye to Reeva in a "proper way".
He broke down when he said Reeva would be sorely missed at family gatherings.
He said her father would spread her ashes during another private service to be held at a later, unspecified date.
After the briefing, reporters hung around on the grass under the trees.
Before the service, a black Mercedes-Benz hearse carrying the model's body stopped at a side entrance to the chapel.
Her coffin, which was draped in a white cloth with an arrangement of white flowers on it, was carried in by hand.
When Steenkamp's parents arrived for the funeral, they had to hoot to make their way through a crowd of reporters partially obstructing the driveway to the chapel.
Disc jockey Thato Sikwane, commonly known as DJ Fresh, of 5FM, and Springbok rugby player Francois Hougaard were among the mourners at the funeral.
Recent media reports claimed Hougaard sent Steenkamp an SMS shortly before her fatal shooting, prompting speculation of a possible love-triangle. Hougaard has denied having anything to do with the case.
The service started at 11am.
At the same time, Pistorius was bringing a bail application in the Pretoria Magistrate's Court.
"The city is in grief, a little angel is no more," said Nelson Mandela Bay deputy mayor and ANC Women's League provincial secretary Nancy Sihlwayi.
She said Pistorius should not receive bail.
Sihlwayi said women needed to be protected by the justice system and she urged men to stand up against gender-based violence.
Pupils of St Dominic's Priory, the school which Steenkamp attended, were also at her funeral.
One said Steenkamp had been "family to the school".
She said she remembered that Steenkamp had "tried to be part of us, made time for us and she even made time to learn to my language" [Xhosa].
A large contingent of local and international media assembled outside the crematorium from early on Tuesday morning.
There was an air of restrained suspense at the tranquil, weather-beaten building, which is surrounded by large trees and terraced lawns, before the service began.
When the police warned news teams to leave the premises, they retreated to outside the boundary wall.
Part of the crematorium, a memorial wall and several gravestones were visible from the entrance, where police had erected a cordon. – Sapa