Cooper Onyett drowned at a Port Fairy indoor swimming pool last week while on school camp with his year two class from Merrivale Primary School.
Under Victoria's seven-day lockdown restrictions, funerals are restricted to 10 mourners, plus those required to conduct the service.
Cooper's family had asked for more people to be allowed to attend the funeral, which was held in Warrnambool, 250km west of Melbourne, on Friday.
Chief Health Officer Brett Sutton confirmed health department staff had spoken to the family, but their request had been declined.
"These are the most difficult decisions for the exemptions team to make and it'll be weighing extremely heavily on them," Professor Sutton told reporters on Friday.
"This is the most tragic circumstance. I can't express enough my sorrow for the family."
Prof Sutton said he did not have a say in the decision and did not know why the request had been declined, but "equity issues" for others holding funerals during lockdown would have been a consideration.
Acting Premier James Merlino also expressed his condolences.
"This is an awfully, awfully tragic case, every parent's worst nightmare," he said.
Southwest coast MP Roma Britnell said she contacted Mr Merlino directly about the family's plight, but the family had still not received a clear answer from the department late on Thursday.
"I understand the Department was busy yesterday, but when you publicly state you are going to call a grieving mother, you make sure you do it and you make sure that call provides the info they need," Ms Britnell said in a statement.
"I'm so deeply sorry that the family has had to go through this on top of everything else they are dealing with and I am thinking of them today as they farewell Cooper."
On Thursday, Cooper's mother Skye Meinen said she was "shocked and angered" by the restrictions on regional Victoria, where there have been no positive cases of COVID-19 in the current breakout.
Relative Tennielle Onyett posted on Facebook that nothing anyone could say would take away the family's pain.
"Oh Cooper ... This wasn't how your life was meant to go. This wasn't how your story was meant to end. You had so much left to do. So much left to achieve. So much left to give," she wrote.
A GoFundMe page set up to help the family cover Cooper's funeral costs has already raised more than $95,000.
