Two men accused of murdering the 27-year-old in January 2011 during her honeymoon were found not guilty at the Supreme Court on Thursday.
The family of Mrs McAreavey, who were left "devastated" by the verdict, are now expected to fly home from the island.
They say they do not wish to discuss the outcome of the eight-week trial.
"Both families have indicated that they will not be making any further comment on the trial or their ordeal in Mauritius," a statement issued on their behalf read.
"They thank people for their support and ask the media to respect their right to privacy as they return home."
UTV's Marc Mallett has spoken at length with DPP Satyajit Boolell following the verdict.
He put it to him that there is a perception in Ireland that the investigation by Mauritian police into the Ballygawley woman's death was shambolic.
"I reject totally these easy, cheap allegations against the police," said Mr Boolell.
I must say that I was bitterly disappointed with the jury's verdict yesterday.
Satyajit Boolell
"The case for the prosecution was based on a confession which was recorded in presence of the counsel for the accused party so we cannot simply dismiss the police investigation.
"I wish I was told the reason what motivated the members of the jury to reach the verdict that they did and I wish that not only for myself, but for the McAreavey and Harte family."
Avinash Treebhoowoon, 32, and Sandip Moneea, 43, both denied killing Mrs McAreavey at the luxury Legends hotel, where they were working at the time.
The jury of six men and three women delivered unanimous not guilty verdicts at the court in Port Louis, to cheers from supporters of the two accused in the public gallery.
The deliberations had taken just over two hours. Relatives of Michaela and John left the courtroom as the men broke down in tears and were released.
Defence for Sandip Moneea and former Attorney General Rama Valayden said the failure to prosecute someone for Michaela's death lies with the police.
"I would say that in fact, it's something that doesn't even smack amateurism," he told UTV.
He explained that even 'amateur' football players play "with a professional mind".
It's not even amateur. I would say that a child of ten years old would have done a better job.
Rama Valayden
Political leaders from across the island of Ireland have shown solidarity with the families in their belief that justice has not been done.
Deputy First Minister Martin McGuinness said: "They should be under no illusion that the people of Ireland will not rest until justice is done.
"Everyone on this island stands shoulder to shoulder with John McAreavey.
"As deputy First Minister I wish to extend my solidarity to John McAreavey and to his family and to Mickey Harte and his family in the wake of this trial and verdict."
Taoiseach Enda Kenny said: "I note the words of the Prime Minister that justice will be done and will be seen to be done, and clearly it hasn't been done.
"A beautiful young Irish woman was murdered and her husband has been out there for the last seven or eight weeks facing the consequences of this trial which brought nobody to justice."
It had been the prosecution case that Treebhoowoon and Moneea killed Michaela when she went to the room to get some biscuits and caught them stealing.
But, by their verdicts, the jury rejected that case.
This is utter devastation, and for John McAreavey himself, this is just so difficult.
Enda Kenny
Treebhoowoon had confessed to the murder during police questioning in the days after Michaela's body was found, but he later insisted he had only done so under torture by the officers holding him.
Meanwhile, a phone call made by Moneea on 10 January 2011, just after 2.45pm - the time Michaela is said to have been killed - was key evidence presented by his defence and accepted by the jury as proof of innocence.
The young bride - the only daughter of Tyrone GAA boss Mickey Harte - was found strangled in their hotel room by her new husband.
The trial has been one of the longest of its kind in Mauritian history and defence lawyer Rayma Valayden has now called for the police investigation to be reopened immediately.
Mr Booleell said that, while that may not happen straight away, he is looking into the circumstances in which could lead to it re-opening.
"Our message to the Harte family is that, and the McAreavey family that we have, our thoughts are very much for them," he added.
"We can tell that we have to accept the system that is in place. It may not have provided results today but we should not lose hope and I know that they are people who are praying for justice.
"Justice will have to be rendered to them eventually."