Scottish Public Services Ombudsman Jim Martin has also said staff at the GP practice should offer to meet with the parents to "re-enforce this apology".
He launched an investigation after the boy's mother, identified as Mrs C, complained about the care her child received.
Mr Martin ruled the practice had failed to provide the boy with "appropriate clinical treatment" and had "unreasonably delayed" referring him to hospital for a specialist opinion.
The Ombudsman's report told how the boy, then aged six-and-a-half, attended the GP surgery several times between May 2011 and September 2011, complaining of weight loss, fatigue, vomiting, nausea and bone pain.
He was seen by a number of doctors there and various examinations and tests were carried out.
When his condition did not improve, he attended Ninewells Hospital in Dundee and then the Royal Hospital for Sick Children in Edinburgh, and was diagnosed with stage four Burkitt's lymphoma - a form of the cancer non-Hodgkin lymphoma.
Despite treatment, the youngster - identified in the report as Master A - died in May 2012.
During the period June 11 to August 24 2011, the boy had 13 contacts with the GP practice. In addition, from late May to late August 2011, NHS 24 were contacted on four occasions about his health and he had two attendances at hospital, the Ombudsman's report revealed.
"This was a total of 19 attendances at healthcare establishments in a young boy who had rarely attended the practice in the six-and-a-half years since his birth," it added.
The report said national guidelines state that in the case of a child or young person presenting several times with the same problem, but with no clear diagnosis, urgent referral should be made.
The guidelines also give specific recommendations for cancers of the blood, such as leukaemia and lymphomas, listing symptoms which should suggest further examination or referral, which include fatigue, weight loss and persistent or unexplained bone pain.
The Ombudsman's report said: "Mrs C was concerned that given Master A's symptoms and his deteriorating condition, the practice should have referred Master A to a specialist sooner. Mrs C said the practice should have recognised that Master A had 'all the red flags' which suggested that he may have had cancer and listened to Mrs C's repeated pleas for them to refer Master A to hospital."
It added: "It is clear that Master A attended the practice several times with the same problems, that Mrs C expressed repeated concerns about his condition, that the symptoms Master A was experiencing were in the list of possible symptoms of cancer and that his health was not improving. All these factors indicate that an urgent referral would have been appropriate."
The report stated that while childhood cancers, particularly Burkitt's lymphoma, are rare, they have a "good prognosis with treatment".
The cancer specialist who saw the boy "stated clearly that his treatment was curative and that he fully expected Master A to have a good prognosis" but unfortunately he was "one of a minority group of patients who did not respond to treatment as expected".
As well as recommending an apology be made to the boy's parents, Mr Martin said the practice should provide his office with evidence that the case "has been discussed with all GPs involved as a learning tool".
The report stated the GP practice had accepted the recommendations and would "act on them accordingly".
NHS Fife said that as GPs are independent contractors, it would be "inappropriate" for the board to comment on a complaint relating to an individual practice.
Dr Stella-Anne Clarke, NHS Fife medical director for primary care, said: "NHS Fife takes all complaints seriously and findings and recommendations made by the Scottish Public Services Ombudsman (SPSO) in every case are always shared so that lessons can be learned by all. Senior NHS Fife staff visit GPs to ensure recommendations are carried out."