A day after reaching a $5.9-million settlement with the city of New York,
"Don't congratulate us. This is not a victory. Victory will come when we get justice," Garner's mother, Gwen Carr, said at a news conference with Garner's widow, daughters and the Rev.
Garner's family again asked for federal investigators to intervene after a local grand jury declined to indict Officer Daniel Pantaleo, who wrestled Garner to the ground in an apparent chokehold July 17.
A bystander's video captured the 43-year-old father of six repeatedly saying "I can't breathe" shortly before his death as police tried to arrest him on suspicion of selling untaxed cigarettes on the sidewalk in the Tompkinsville section of Staten Island.
Garner's death was ruled a homicide. The Department of Justice opened a federal civil rights investigation into the case after the local grand jury decision in December, which prompted widespread protests.
Further demonstrations are planned in New York on Saturday, a day after the anniversary.
"Eric Garner and the community have not received justice," Sharpton said at the news conference. "Money is not justice. Money is a recognition of the loss of the family, but it does not deal with the criminal and other wrong done to this family and other families."
Garner's wife, Esaw Garner, said police "treated my husband like an animal, and I think they give animals more respect."
"I can't sleep at night. I've been married 28 years," she said. "Now I have no one but my children, and I am alone to deal with this for the rest of my life."
Garner's daughter, Erica Garner, said the $5.9-million "does not represent justice" and that "no amount of money is going to bring my father back."
Jonathan Moore, a civil rights attorney who is representing Garner's family, said Monday that the settlement was the biggest ever for the city in a case of its nature.
Garner's relatives also reached a settlement with Richmond University Medical Center for a confidential amount, Moore said. The family sued the medical center, which provided the first responders, alleging poor care of Garner at the scene.
In announcing the city's settlement on Monday evening, New York City Comptroller Scott Stringer said the amount "acknowledges the tragic nature of Mr. Garner's death while balancing my office's fiscal responsibility to the city."
The agreement settles a claim for damages related to Garner's death sought in a lawsuit his family filed against the city last year. The city admitted no liability.
On Tuesday, the leader of one of New York's police unions blasted the settlement as "obscene" and asked, "Where is the justice for New York taxpayers?"
"While the death of Mr. Garner while resisting arrest was unforeseeable, this excessive and exorbitant settlement was not," Ed Mullins, president of the Sergeants Benevolent Assn., wrote in a column for the New York Post.
"Although Mr. Garner did not provide his family with an abundance of wealth, it was clear from the outset that the mayor's office would," Mullins said. "Mr. Garner's family should not be rewarded simply because he repeatedly chose to break the law and resist arrest."
Relations between New York's police unions and New York City Mayor Bill de Blasio have been raw since Garner's death. The unions took particular exception to statements de Blasio made that were sympathetic to protesters critical of police.
The decision not to indict Pantaleo in December came nine days after a grand jury in Missouri declined to charge a white officer in the death of Michael Brown, an unarmed black 18-year-old who was shot and killed on Aug. 9 by a white officer in Ferguson.
Both grand jury decisions sparked a tide of anger and a wave of protests around the nation.
Garner's family members and Sharpton said Tuesday that they would continue their call for justice at several events scheduled this weekend.
The main event is a "justice" rally on Saturday in front of the federal courthouse in Brooklyn, where the U.S. attorney's office is also housed.
Two church services also were planned for Friday, the anniversary of Garner's death.
One will be held at the New Canaan Church of Christ in Harlem and another at the House of the Lord Church in Brooklyn.
Sharpton and Mayor Bill de Blasio were also set to attend a prayer service Tuesday night at a Staten Island church.