The Scottish Public Services Ombudsman ordered the apology three years after the allegations first surfaced at an independent school in the west of Scotland.
The family were not satisfied with the way the un-named school dealt with the complaint.
The pupil's father, Mr C in the report, raised concerns that his son was bullied by pupils involved in the allegations.
And he alleged that one reason why not enough was done was that one of the other pupils involved was the son of a member of the school board.
He reported the matter to the Scottish Government's learning directorate – where the Registrar for Independent Schools in Scotland is based.
The registrar investigated the complaint and, as a result of its findings, the Scottish Government rejected calls for further investigation. The family then made a complaint to the ombudsman because of concerns over the way the matter had been dealt.
Jim Martin, the ombudsman, has upheld the complaint, although he stressed the issues of concern would not have led to a change in the advice from the registrar that no further investigation was required.
Mr Martin said: "This has been a difficult and arduous process. Despite initially complaining when the decision was issued in September 2010, and attending a meeting with the registrar, Mr C was not signposted to the complaints process until March 2011.
"I upheld Mr C's complaints that the registrar unreasonably failed to undertake a thorough investigation of his complaint ... and that the registrar's report was based on factually incorrect information.
"I suggested that the registrar could have been more robust in his approach and could have sought clarification from the department ... and the reporting guidelines set out in the National Guidance for Child Protection in Scotland.
"I also noted a number of inconsistencies between the school's records and the report referred to by the registrar in his advice to ministers, and noted that the learning directorate accepted that there had been inconsistencies.
"I am not suggesting that, had these failings not taken place, the registrar's advice to ministers would have changed."
The family had two complaints upheld by Mr Martin, who told the learning directorate to tighten up its procedures and to apologise to the pupil and his father over the way the registrar handled the case.
Mr C said the case had been an exceptionally difficult and distressing one for his family.
Mr Martin added: "I made a number of recommendations for redress, including that the learning directorate ensure that written procedures are in place for investigating and reporting to ministers; ensure that any recommendations made by the registrar in relation to such a request; draw the findings of this investigation to the attention of the registrar; and apologise to Mr C .... for the failings identified in my report."
The directorate has accepted the recommendations and will act on them accordingly.