NEW YORK (CBSNewYork)Eric Garner‘s family says the NYPD’s decision to fire NYPD officer Daniel Pantaleo is only part of the justice they’ve waited five years for.

For them it still feels like incomplete justice.

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In 2014, a Staten Island grand jury refused to indict Pantaleo on criminal counts.

Then a five-year review by the Obama and Trump Justice Departments ended with no civil rights charges.

The Garners did collect almost $6 million in a wrongful death settlement with New York City.

Emerald Garner, who believes her father was murdered, takes some measure of satisfaction in Monday’s decision.

“Commissioner O’Neill, I thank you for doing the right thing,” she said Monday. “I truly sincerely thank you for firing the officer. Regardless of how you came up to your decision, you finally made a decision that should have been made five years ago.”

Gwen Carr, Garner’s mother, stood before NYPD headquarters Monday afternoon to say her fight for justice is not over.

“Yeah, Pantaleo, you may have lost your job, but I lost a son,” she said.

Carr says the other officers involved that day should meet the same fate as Pantaleo.

“We have other officers that we have to go after. You have heard the names. We know the wrongdoing that they have done,” she said. “New Yorkers are not safe with officers out here like that.”

The police union leadership is portraying the firing as a betrayal by top NYPD brass, claiming Commissioner James O’Neill buckled to political pressure from Mayor Bill de Blasio.

“To stand and watch the press conference by the police commissioner to basically say that he followed the politics rather than the rule of law and the evidence is absolutely embarrassing,” said Pat Lynch, president of the Police Benevolent Association.

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In a memo to membership, Lynch told cops “for every job involving a possible arrest situation, immediately request (a) response by (a) patrol supervisor and additional members to help control (the) situation” – an approach which could significantly slow down the rate of arrests.

Those who advocated on Garner’s behalf say Lynch is out of line.

“Pat Lynch, you are trying to bring us down a very dangerous road. Do not ask officers not to do their jobs,” NYC public advocate Jumaane Williams said.

The mayor vowed that will not be tolerated.

“The people of this city will not accept any work slow-downs by any public servants,” de Blasio said.

Rev. Al Sharpton slammed the PBA for labeling those who wanted Pantaleo fired as “cop haters.”

“No, we expect more of police and we have the right to expect that at least they’re going to follow the guidelines that they were trained on,” he said.

Sharpton says he wants the House Judiciary Committee chaired by Rep. Jerrold Nadler of New York to look at all the circumstances of the Eric Garner case.

The Garner family is also pushing for a ban on all chokeholds in state law rather than having them addressed administratively in patrol guides.

It seems all sides remain unsatisfied with the decision in some way, although Dr. Henry Smart III, a John Jay criminal justice professor, believes most officers likely agree with it.

“Most public organizations are filled with folks who have good intentions, right? And now secretively, I think they’re saying, yes, this will now help our department,” Smart said.

CBSN New York’s urban affairs expert Mark Peters points out many know they could have been in those same shoes.

“Being a police officer is one of the hardest jobs in the world … so I think what you’re seeing is a police officer, any police officer, thinking, that could’ve been me,” Peters said.

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Monday evening, the union that represents FDNY EMS issued a statement to its members saying they believe Pantaleo’s firing has made their jobs more dangerous and will embolden criminals.