First-team coach Andy Smith, goalkeeping coach Marco Tabuas and fitness coach Maykel Moreira have now also left Vale Park, the League One club has confirmed.
The three all arrived when Ribeiro was appointed in the summer.
"We thank them for their time with us," a club statement said.
"They helped assist the club to their best home start to a season ever at Vale Park and progression to the FA Cup third round."
Vale face a home game with Chesterfield on Friday before a trip to Oldham on Monday, prior to playing Championship side Huddersfield Town in the FA Cup on 7 January,
They have lost their last three league games to slip to 17th in the table - just six points above the relegation zone.
Ribeiro's former assistant, Michael Brown, has been placed in temporary charge of the Burslem-based club.

A total of 76 suspects have been arrested and huge quantities of drugs and arms seized in a series of raids.
The ring used backpackers and vehicles to smuggle marijuana, cocaine and heroin across Arizona's western desert.
The network was linked to Mexico's Sinaloa cartel and generated an estimated $2 billion in profit over the last five years, officials said.
"Today we have dealt a significant blow to a Mexican criminal enterprise that has been responsible for poisoning our communities," said Arizona Attorney General Tom Horne.
"I find it completely unacceptable that Arizona neighbourhoods are treated as a trading floor for narcotics", he added.
The bust - known as "Operation Pipeline Express" - followed a 17-month investigation by multiple US law enforcement agencies.
A mix of US and Mexican nationals were arrested in three sweeps last week, earlier this month and in September, officials announced.
More than 30 tons of marijuana, 90kg (200lbs) of cocaine and 72kg (160lbs) of heroin were seized, as well as more than 100 firearms.
Operating from the Arizona towns of Chandler, Stanfield and Maricopa, the network ferried drugs across the Mexican border on foot and by vehicle to safe houses in the Phoenix area, officials said.
The drugs were then sold to criminal gangs who distributed them in other states across the US.
Officials believe the network made huge profits by securing a monopoly on smuggling routes along an 80 mile (128km) stretch of the remote desert border from Yuma to to the community of Sells in the Tohono O'odham Indian reservation.
Intelligence suggested the ring was linked to the Sinaloa cartel, led by Mexico's most-wanted fugitive drugs lord, Joaquin "El Chapo" Guzman.
"We in Arizona continue to stand and fight the Mexican drug cartels, who think they own the place," Pinal County Sheriff Paul Babeu said.
"This is America and we shall bring a crushing hand of enforcement against those who threaten our families and our national security".

The Accounts Commission said there was a risk services could not be maintained without improvements in the way the council was run.
But the report recognised that the council delivered good services at the moment.
The authority needs to save Â£22.3m - 10% of its budget - by 2017/18.
On top of that, council reserves are low and are projected to fall further, the report said.
The Accounts Commission is the public spending watchdog for local government in Scotland.
In its report, the commission said the council urgently needed "clearer priorities" in its transformation programme to ensure key projects were completed and savings made.
The report recognised the council's "commitment to improvement", but added that it was concerned about the pace of those improvements.
Deficiencies highlighted by the commission included financial control and management of resources.
The chairman of the commission, Douglas Sinclair, said: "There is a gap between the council's ambition and seeing evidence of that on the ground. This is what East Dunbartonshire needs to address if it is to continue to deliver good quality services in the future."

It happened at about 12:30 BST. The victim died at the scene.
Another man is in a critical condition.
The road is expected to remain closed for a number of hours while a thorough investigation into the crash is carried out.
Port Vale have parted company with three of their backroom staff after manager Bruno Ribeiro's Boxing Day departure.
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US authorities say they have broken up a massive drug-smuggling network run by a Mexican cartel in Arizona.
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A public spending watchdog has published "serious concerns" over the financial control of East Dunbartonshire Council.
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A man has died following a two-vehicle collision on the A1 carriageway at Banbridge on Tuesday.