Rangers avoided relegation by finishing 10th but the club was later charged for failing to implement Haveron's touchline ban against Dungannnon.
It could have resulted in Carrick losing three points and being relegated but the Irish FA decided not to apply any sanction following a hearing.
Haveron replaced Michael Hughes as Rangers boss in September 2013.
"The Board of Carrick Rangers FC can announce that we have accepted the resignation of manager Gary Haveron and assistant manager Steven Mills," said the club on Monday.
"Following discussions between the Board and the management team, we were unable to establish a mutual agreement on the best way forward for the club."
He guided Carrick to Championship success in his first full season and with it a return to top-flight football.
Last month's dramatic 2-1 victory over Ballinamallard United on the final day of the season moved Carrick from the bottom to 10th and safety.
Their Premiership status was threatened by the touchline charge but the IFA Disciplinary opted to "exercise its discretion" in not imposing a sanction.
Warrenpoint Town, who finished bottom but just a point behind Carrick, have appealed the IFA ruling.

Gustavo Silva Da Cruz was among three swimmers seen struggling in the water around noon on Sunday at Camber Sands.
He was discovered on the beach at 18:20 BST and declared dead at the scene. Police said he had been visiting family in Croydon, south London.
The others - a man and his teenage son - are critical but stable in hospital.
The pair, who are aged 35 and 17 and from London, were not connected to Mr Silva Da Cruz.
They were given CPR by paramedics and airlifted to hospital.
Live updates after swimmer's body discovered
A Go Fund Me website appeal has been set up to raise funds to return Mr Silva Da Cruz's body to Brazil.
It says he was in the UK to visit his father and family, who are originally from Brazil.
He was raised in Brazil by his grandparents and mother.
The website said: "The family was enjoying the hot weather in the company of friends at Camber Sands beach where Gustavo drowned.
"The young man was dragged by the strong wind which started suddenly and could not swim back to the beach."
More than 1,000 people have signed a petition calling for lifeguards to be located at Camber Sands.
Rother District Council said it was saddened by the incident and its thoughts were with the families and friends of those affected.
It said the beach was "particularly busy with around 25,000 visitors" on Sunday.
"As is usual for the summer season, beach patrols were on site to advise people of potential dangers, reunite lost children and deal with incidents on the beach.
"The district council's coastal officer and officers from Sussex Police were also on the beach."
A spokesman said: "Our officers are trained to deal with incidents on the shore and acted quickly and professionally in what was an extremely distressing situation; performing CPR on two of the men and alerting HM Coastguard and the RNLI who carried out the search for the missing man."

Arthur Simpson-Kent left the UK on 19 December after the deaths of Ms Blake, 43, and their two young sons, Zachary, aged eight and Amon, aged four.
Their bodies were found buried in the garden of their family home in Erith, south London, on 5 January.
Mr Simpson-Kent is due at Westminster Magistrates' Court on Friday.
Ms Blake, who played Frankie Pierre in 56 episodes of EastEnders in 1996 and 1997, died from neck and head injuries, post-mortem tests found. She had been suffering from motor neurone disease.
Her sons also died from head and neck injuries.
Four days after their bodies were found, police officers arrested Mr Simpson-Kent on a beach in Ghana.
He was remanded in custody in Ghana on 12 January and appeared in Kaneshie Magistrates' Court in Accra.
Mr Simpson-Kent was arrested after locals recognised him from a social media photo and tipped off police.
The Met was criticised over delays in its investigation after it emerged officers spoke to Mr Simpson-Kent at the family home on 16 December.
They returned two days later to find the house empty.
But it was not until early January that the bodies of Ms Blake and her sons were found in the garden.
The Met's handling of the case is being investigated by the Independent Police Complaints Commission.
Gary Haveron has resigned as manager of Premiership side Carrick Rangers after a controversial end to the season.
[NEXT_CONCEPT]
A man who died after two others were pulled from the sea off East Sussex has been identified as a 19-year-old Brazilian national.
[NEXT_CONCEPT]
The partner of EastEnders actress Sian Blake, whose body was found in their garden, is to be flown back from Ghana to the UK later, prosecutors have said.