Surrey Police said they accepted "mistakes were made" in the original investigation into Cheryl James' death at Deepcut.
But they insisted her death has now been the subject of a thorough investigation.
And as Detective superintendent Adam Hibbert, from Surrey Police, delivered the prepared statement on the steps outside Woking Coroner's Court he was met with a shout of "liar".
DSI Hibbert said: "The death of Ms James has been a tragic loss of a young woman's life, and we recognise that this has been compounded for her family and friends as a result of the way her death was subsequently investigated.
"Surrey Police has long accepted that mistakes were made in this investigation. The force should have maintained primacy for it, and has previously apologised to the family for those errors.
"Today we would like to reiterate those apologies."
Backing the coroner's investigation, he added: "We know that Ms James' family have long since been seeking answers to the circumstances surrounding her death.
"The evidence has now been thoroughly examined throughout the new inquest today, and our thoughts are with Ms James' family and her friends. We hope they can take time to reflect upon the coroner's verdict.
"We are also acutely aware that today's findings will be relevant to the families of the other three young soldiers who died in Deepcut barracks between 1995 and 2002.
"I would like to take this opportunity reassure them that we will fully support any need for disclosure for any future potential coronial processes."
But as he walked away from the court steps there was a shout of "liars".