Robert Buckland QC has acknowledge Government cuts have played a role in the current problem, that sees fewer than five per cent of rape cases reported to police resulting in somebody being charged.
The issue has previously been described by Victims Commissioner Dame Vera Baird as effectively "decriminalising rape".
A Government review was published this week into the Criminal Justice System's (CJS) handling of rape cases after a two-year wait, with many campaigners against violence against women and girls saying it did not go into enough depth.
Speaking to BBC's Laura Kuenssberg, Mr Buckland admitted the current problem was "not good enough" and that major changes - both cultural and financial - were needed.
“Like all parts of public service big choices were made in the last decade, because of the position that we all faced economically and that’s, I think, self-evidently the case,” the QC told BBC political editor Laura Kuenssberg.
Mr Buckland said the Government was now “seeking to make the necessary investment”, but added it was also “about more than just money, it’s about culture”.
“The first thing I need to say is sorry,” he said.
“It’s not good enough. We’ve got to do a lot better. And the plan that we are outlining in that review is all about taking practical steps to change the situation and to address the causes for this failure.”
Speaking to The Yorkshire Post, Katie Russell from Rape Crisis England & Wales said that while there were "positives to be taken" from Mr Buckland's admission, the issue of justice for sex offence victims came about as a result of many reasons beyond funding.
"Words are important so it's important that the Government has apologised and recognised the systemic failures," she said.
"But we are disappointed that this review behind the apology doesn't go into enough depth and still doesn't effect the changes we urgently need to see.
"There are clearly wider systemic issues at hand in the prosecution of sexual offence cases, and as these crimes predominantly affect women, you can't help but wonder there is still misogyny ingrained in our justice system."
Sharon Bryan, from the National Centre for Domestic Violence, called the Government review "woefully unambitious" and a "squandered opportunity to map this sorry and shameful state of affairs".“Although we would normally be the first to welcome a Government review of rape, this report represents a squandered opportunity to map this sorry and shameful state of affairs.
"Its recommendations fall well short of an effective programme of reform, it will allow many more perpetrators to escape justice and leave yet more victims devoid of redress and practical help," she said.
The review includes a raft of measures intended to see the volume of allegations referred by the police to the Crown Prosecution Service (CPS), the number of suspects charged, and the amount of cases reaching court return to 2016 levels by the end of this Parliament.
Measures include a pilot scheme aimed at reducing cross-examination of victims in court by conducting pre-recorded interviews, a nationwide recognition that only evidence about the complainant that is pertinent to the case should be used, and a new approach to investigations which ensures that there is an “early and robust assessment of suspect behaviour and offending patterns”.
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