The move means setting aside a controversial 2012 report from former Canadian Supreme Court judge Justice Ian Binnie.
Mr Karam said while he disagreed with the need for a new inquiry, Ms Adams had been put in a ''terrible position'' by former justice minister Judith Collins, who oversaw the Binnie report.''
What Collins did is the cause for all of this.''
''It's obviously terribly unfortunate from a number of points of view - the taxpayer forking out another half a million to a million dollars,'' Mr Karam said.
In 2009, Mr Bain was acquitted of five counts of murder, after being sentenced in 1995 to life imprisonment for the murder of his family in Dunedin the year before.
Ms Adams announced yesterday the Government had agreed to set aside all previous advice relating to Mr Bain's compensation claim and conduct a fresh inquiry.
In 2011, former Justice Binnie was appointed to provide advice on the claim.
He completed his report in August 2012, which recommended Mr Bain receive compensation for a wrongful conviction and 13 years in jail.
The report said while his innocence had not been established beyond a reasonable doubt, it was ''more likely than not'' he was innocent.
After being made aware of concerns raised about Justice Binnie's report, and receiving advice from the Solicitor-general, Ms Collins decided to seek a peer review by former High Court judge Dr Robert Fisher.
Dr Fisher found Justice Binnie's report contained a number of errors and was, therefore, unsafe to rely on.
Ms Adams said given those events, ''it's my view that Cabinet doesn't have the information in front of it on which it could reasonably reach a decision''.
''For that reason, the advice of both Justice Binnie and Dr Fisher will be set aside and I will appoint a new inquirer to conduct a fresh inquiry into Mr Bain's claim.''
Ms Adams said she would now seek advice on an appropriate inquirer and develop terms of reference.
Mr Karam said from a political point of view, he could understand ''that she would want to get something which doesn't appear controversial''.
''The only point about that is it just has to be someone from overseas who has never heard of the Bain case to do this, because otherwise, really it's just a waste of time.''
Ms Adams said she had notified Mr Bain's representatives, and understood they were ''comfortable with the process''.
But Mr Karam said that was not the case.
''No. It's like when someone holds a gun to your head and and says 'do this' - well, you're comfortable to do it 'cos you'll get shot if you don't.
''We accept that this is the decision she has made. We certainly don't agree with the fact that there is a need for it, but she holds all the cards, and it's a discretionary matter for Cabinet, and we have to play the game.
''So long as she appoints someone totally independent, I'm 100% certain that the result will be exactly the same, and I trust this minister to react in a proper way.''
He said it was likely Mr Bain would be required to makes submissions to a new inquiry.
''I presume it will be like a fresh start.''
Mr Karam said he had not yet discussed the matter with Mr Bain.
