Esaw Garner, wife of Eric Garner, speaks alongside Garner's mother, Gwen Carr
Esaw Garner, his widow, wept as she said: "My husband is now six feet under and I'm looking for a way to feed my kids." She also asked the question, who's gonna play Santa Claus for their kids this year?
Officer Daniel Pantaleo had earlier offered his "personal apologies" to the family for their loss.
Asked her if she would accept the 29-year-old police officer's condolences, Garner said: "Hell no. The time for remorse was when my husband was yelling to breathe ... when he was screaming 11 times that he can't breathe."
Garner's stepfather, Benjamin Carr, urged calm but said the ruling made no sense.
"It's just a licence to kill a black man," he said, calling the justice system "not worth a damn". Following yesterday's grand jury decision, Attorney-General Eric Holder said the US Justice Department would launch a federal civil rights investigation into the case of Garner, who died after being placed in a chokehold by Pantaleo while being arrested on suspicion of selling untaxed cigarettes on Staten Island.
That did not deter protesters in Times Square, who waved signs with messages such as "Black lives matter", and "Respect human lives". Several people were arrested in protests near the Rockefeller Centre.
There was another protest in the great hall of Grand Central Station, where about 50 protesters lay, pretending to be dead, and on Staten Island. There were small peaceful protests in Washington, DC.
Garner's death is one of a string of high-profile, racially charged incidents in which white officers have been accused of using unreasonable force or being too quick to fire at black suspects.
In comments after the grand jury decision, President Barack Obama addressed the inherent mistrust many African Americans have of police. "We're seeing too many instances where people do not have confidence that folks are being treated fairly," Obama said.
"In some cases, those may be misperceptions, but in some cases that's a reality, and it is incumbent upon all of us as Americans ... that we recognise this is an American problem and not just a black problem or a brown problem."
The August shooting death of 18-year-old Brown by a white officer in Ferguson, Missouri, sparked consecutive nights of violence and has become a rallying cry for African-American communities across the country fed up with what they say is racially biased policing.
A grand jury in that case also decided not to charge the officer involved.
"Today's outcome is one that many in our city did not want," said New York Mayor Bill de Blasio, who was quick to call for calm.
"New York City owns a proud and powerful tradition of expressing ourselves through non-violent protest. We trust that those unhappy with today's grand jury decision will make their views known in the same peaceful, constructive way."
In recent days protesters have demonstrated - largely peacefully - in New York to decry what they say is the over-reliance of aggressive tactics by police.
Bill Bratton, the city's police commissioner, said people were welcome to demonstrate. But he warned: "If they engage in criminal activity, such as vandalism - actual crime - they will be arrested."
A New York City medical examiner had ruled Garner's death a homicide caused in part by the chokehold used during the arrest.
De Blasio has said authorities need to address the "underlying reality" highlighted by the deaths of Brown and Garner. De Blasio, who is white, has a mixed-race son and said he is well aware of the difficulties young black people can face.
"We've had to literally train him, as families have all over this city for decades, in how to take special care in any encounter he has with the police," the mayor said.
De Blasio noted that America was "dealing with centuries of racism".
Benjamin Crump, the attorney for the Brown family, said the recent incidents were undermining trust in the US justice system.
"Why are police officers always given special treatment and not held accountable, especially in minority communities?" he asked on CNN.
Meanwhile, New York authorities yesterday announced a pilot programme to equip about three dozen police officers with body cameras to record their behaviour towards the public.
De Blasio hailed the tool as "one of the ways to create a real sense of transparency and accountability".
Garner's family in October said they would sue the city and police for US$75 million ($96.7 million).
- Telegraph Group Ltd
