The former Environment Secretary was appointed to the top job at the Ministry of Justice, also becoming the first ever woman Lord Chancellor, last week.
But a former justice minister, Lord Faulks, resigned following her appointment, which he claimed could be “damaging” to the justice system.
There have also been claims that a second ex-minister refused to serve under Ms Truss.
And another senior Conservative, Bob Neill, who chairs the Commons’ justice committee, told the Guardian he was concerned about whether her lack of experience would enable her to properly represent the judiciary within government.
He said: “I have a concern, with no disrespect to Liz, that it would be hard for someone without that history to step straight in and fulfil that role.”
But supporters of Ms Truss were quoted describing the comments as “thinly veiled misogyny”, an accusation Mr Neill denied.
And Ms Truss’ office have insisted it is “business as usual” as she signalled her intention to press ahead with prison reform proposals.
The comments followed the publication of the annual report by the chief inspector of prisons, Peter Clarke, which showed soaring levels of violence, self-harm and deaths in English and Welsh jails.
Incidents of assaults rose by 27 per cent last year, while cases of self-harm and self-inflicted deaths among inmateswere also up by 25 and 27 per cent respectively.
Mr Clarke said he had also been struck by the numbers of inmates battling mental health problems.
And he admitted: “There is a simple and unpalatable truth about far too many of our prisons.
“They have become unacceptably violent and dangerous places.”
Ms Truss, who visited the Belmarsh and Isis jails on her first full day as Justice Secreytary, said the report showed why change was so urgently needed.
She said: “I want to see radical reform and I am under no illusions about the scale of the challenge we face.
“I will set out the next steps for this agenda in the coming weeks, but I am clear that the vital work of prison reform will continue at pace.”