The family of Eric Garner vows to continue their fight for justice after federal prosecutors decided not to charge a New York City police officer in his choking death.

Garner died exactly five years ago during an arrest for allegedly selling illegal cigarettes on Staten Island, after police officers knocked him to the ground and put him in a chokehold. His death ignited demonstrations nationwide, and his dying words, "I can't breathe," became a rallying cry in protests against police violence.

Federal prosecutors said on Tuesday that evidence does not prove the officers willfully violated Garner's civil rights. His daughter and mother gave emotional responses to the decision soon after – and in an interview with "CBS This Morning" Wednesday, Garner's mother, Gwen Carr, slammed the Department of Justice and New York City mayor Bill de Blasio for failing to hold the officers accountable.

A day after the DOJ's decision, Carr said that the wound is still fresh – especially because July 17 is the fifth anniversary of Garner's death. "It's still insult to injury that they're not going forward with charges, saying that the bar was too high to bring charges against them," Carr said.

It's still possible that Police Commissioner James O'Neill could pursue disciplinary actions against the officer, Daniel Pantaleo – and Carr said she hasn't yet given up hope.

"I'm just hoping Commissioner O'Neill does the right thing," she said. "We've been failed by every other source: the de Blasio administration has blocked us up until this point – so I want the de Blasio administration to step up. Because he can fire the officer at any time."

If Pantaleo is fired, Carr said, it will give her some closure – but it won't bring her son back. "It won't be justice for Eric, because Eric is gone," she said. "There is no justice for Eric."

So far, not a single officer on the scene that day has been disciplined.

Carr also slammed federal prosecutors for allegedly leaking information about their decision before meeting with Garner's family. "We didn't find out until the afternoon on Monday that they wanted to speak with the family – so now, they say they want to speak with the family, and then afterwards, have a press conference," Carr said. The family thought they were going to get "positive" news – but while they were waiting to speak with prosecutors, she added, they found out about the DOJ's decision on social media.

"The whole world heard the decision before we did," she said. "The whole world."

Pantaleo's attorney Stuart London said in a statement that his client "is gratified that the Justice Department took the time to carefully review the actual evidence."

Carr is more doubtful about the veracity of the review. "This was all political," she said. "Because from the beginning, they brought in a medical examiner that had nothing to do with the case – brought him in from Missouri… for the autopsy. The actual medical examiner told them it was a chokehold. It was a lethal cascade, that's what she called it, a lethal cascade." Carr also claimed that the paid examiner never looked at the autopsy.

Carr added that watching the tape of her son's death is still extremely painful. "That tape – it just tears me apart every time I look or hear the sounds…" she said. "I see them killing my son and they're not letting him up. I can't even look at the tape in its entirety."

"How do you forgive someone who has taken your child's life?" she added. "I hear people say they forgive, I know as a Christian, you're supposed to forgive – but I'm sorry, I'm not at that space yet."

For Carr, closure would mean "the officers – all of them, that day – standing accountable for what they did to my son that day."

"Even if he was selling cigarettes, it is not a death sentence," she said. "My son should not have died that day."