Pvt Kovco died in a fatal shooting in his Baghdad barracks on April 21. The repatriation of his body to Australia was subsequently bungled.
Today the widow made it clear that the many apologies over the incidents did not placate her or her two young children, Tyrie and Alana.
Mrs Kovco said there had been "one mistake after another" by the army and the federal government since her husband's tragic death, including a failure to secure vital evidence at the scene and the mix-up over the return of his body.
"I would like to say how sick I am of hearing sorry for these mistakes," she told the inquiry.
"Sorry doesn't cut it after the first time.
"Nothing in the world can make things okay for us now.
"Our lives changed on the 21st of April and will never be the same again, and I just hope there is some light at the end of the tunnel for the kids and me, whatever that may be."
Media criticised
Mrs Kovco also lashed out at the media for invading her privacy since her husband's death, and called on the inquiry to return all his personal items tendered in evidence, including a laptop computer.
She also criticised the inquiry for making public, sections of Pte Kovco's journal written one month before his death in which he described a dream he had about shooting himself in the head.
Mrs Kovco also demanded the defence force cancel its contract with private contractor Kenyon International, hired to repatriate Pte Kovco's body.
She said she was horrified when she saw pictures of the civilian morgue in Kuwait that Kenyon used as part of the repatriation process.
The military also needed to improve the way it investigated soldiers' deaths and improve measures to secure incident scenes, she said.
Supported by her mum and dad, David and Lorraine Small, Mrs Kovco sobbed as she read her five-page statement in the inquiry's small hearing room at Victoria Barracks in Sydney.
Nearby were Pte Kovco's own parents, Judy and Martin Kovco, who also shed tears as they listened to their lawyer, Lieutenant Colonel Frank Holles, suggest that no-one will ever know why or how Pte Kovco was shot, given the unreliability of key witnesses and mistakes made by military police who investigated the shooting
scene.
Perhaps the only comfort for Pte Kovco's parents and widow today were to be found in brief comments made by the inquiry's president, Group Captain Warren Cook, who indicated he did not believe the 25-year-old Victorian soldier had deliberately killed himself.
"I don't think the word suicide figures in our reasoning whatsoever," he said.
The Kovco family will have to wait at least six weeks to find out exactly what Group Captain Cook believes may have happened.
'Military incompetence'
Earlier, Pte Kovco's parents Judy and Martin Kovco sobbed as their lawyer, Lieutenant Colonel Frank Holles, told the inquiry the incompetence of military police investigating the private's death, and unreliable witnesses, mean his family will never know how he died.
Lt Col Holles said there had been systemic failures relating to the investigation of how Pte Kovco was shot in the head with his own 9mm Browning pistol.
He accused military police investigators of being incompetent for their failure to preserve vital forensic evidence and for "templating" witness statements for soldiers interviewed about the shooting.
He also accused Pte Kovco's two roommates, Pte Ray Johnson and Pte Rob Shore, of being unreliable witnesses over their claims that while they were with their friend when he was shot, they did not see what happened.
Their colleague, Pte Steve Carr, was also attacked by Lt Col Holles as an unreliable witness, especially because he had not been able to explain how his DNA ended up on Pte Kovco's pistol.
Stolen property
Meanwhile the lawyer representing Pte Kovco's interests at the inquiry, Colonel Les Young, has said police should investigate whether broadcaster Derryn Hinch received stolen property, when he was given a draft report on the bungled repatriation of the Private.
Defence force chief Air Chief Marshal Angus Houston was forced into an embarrassing apology in May after revealing a senior officer had left a CD containing the draft report at Melbourne Airport.
The person who found the CD in a Qantas Club lounge computer at the airport handed it to Hinch, who then broadcast parts of its findings.
Delivering his closing arguments to the board of inquiry, Col Young said the board should refer the case of the lost CD to police, whom he said should determine if the person who found the CD and passed it on to Mr Hinch had "committed an offence of stealing by finding".
Mr Hinch also should be investigated to determine if he had received stolen property, Col Young added.
Board president Group Captain Warren Cook made no comment about Col Young's requests.
He and his fellow board members have now ended the inquiry's public hearings into Pte Kovco's fatal shooting.
The board will now take about six weeks to prepare a report on its findings for Air Chief Marshal Houston.