"We're not embarrassed by the fact he is gay. I just feel personally they didn't do enough to support him. My feeling is perhaps he lacked access to the assistance he deserved. I don't think we've been told the truth," Mr Poa said.
Corporal Hughes' mother, Venus Poa, is expected to return from a trip to Australia today.
Mr Poa said the family planned to meet and discuss what steps to take now that there would be no coronial inquiry.
"I just want to get to the bottom of things. The army have abdicated their responsibility."
He said the family had hoped the coronial inquiry would satisfy their questions and he was angry Mr Matenga had decided not to hold an inquest.
"It's his job to do an investigation."
Former Defence Minister Phil Goff has backed the family.
"I'm not throwing the blame on any particular individual on this," said Mr Goff, Labour's defence spokesman. "I'm just saying that when you have a tragedy of this nature, it's really important to learn all of the lessons of it so you can avoid it happening again.
"Only if you bring it out in the open can you seriously start to address it."
Mr Goff wants the decision overturned by the Chief Coroner or Solicitor-General, as is possible under the Coroners Act.
Corporal Hughes was serving at Romero base in Bamiyan province at the time of his death on April 3 last year.
"This is not about a witch-hunt. It is about finding answers which will assist the Defence Force to help prevent a death of this nature again," Mr Goff said.
"You need to get to the bottom of it, and frankly there are times when it is better dealt with outside of the Defence Force than simply through a Court of Inquiry."
The family reportedly believe Corporal Hughes was bullied because he was gay and received no support from commanders.
But Defence Minister Jonathan Coleman said he did not believe anything could have been done to prevent the tragedy.
Asked about the Defence Force attitude toward gay personnel, Dr Coleman said he did not have concerns about the force's attitude but could not account for the attitudes of every person in the organisation.
The Defence Force has had a policy of accepting gay personnel in line with the decriminalisation of homosexuality in 1986 and the Human Rights Act 1993.
Coroner Gordon Matenga, who declined a full inquest into the suicide of Corporal Hughes, is a Mormon church elder who last year attacked gay marriage in a submission to Parliament, saying it was an unnecessary "social experiment".
Mr Matenga's submission brought a rebuke from Attorney General Chris Finlayson, who told him it would be wise for members of the bench to avoid submitting on issues that could be seen as politically contentious. APNZ
