Richard Keen QC, who has been in his new post for less than a month, is said to have criticised the Labour heavyweight at an event in his townhouse earlier this month.
Keen - dubbed The Rottweiler for his aggressive courtroom appearances - was unveiled by Scots Tory leader Ruth Davidson as her party's chairman last year.
He started work in January and it was hoped he would help bring focus to a job widely regarded in political circles as a poisoned chalice.
It is also a crucial appointment, being in the year of the independence referendum.
However, Keen has been accused of making a gaffe in one of his first key outings in the role.
The lawyer recently hosted a meet-and-greet for the party's MSPs at his £1.7 million home in Edinburgh's Ann Street, which boasts five bedrooms, a library, wine cellar and a conservatory.
It was supposed to be a non-controversial affair, in which Keen would introduce himself, but MSPs were surprised when he attacked Darling, who chairs Better Together.
One source said: "He was pretty scathing about Alistair Darling."
It is understood Keen made reference to the MP's presentational skills.
A second source confirmed Keen's criticisms.
The remarks are controversial as the Conservatives and Labour are the key elements of Better Together.
The incident being leaked is somewhat ironic, as the Sunday Herald understands Davidson hoped Keen's arrival would put an end to leaks.
Keen's barbs appear to confirm scepticism in some Tory circles about Darling's suitability for his role.
One newspaper recently quoted a member of the Tory high command as saying: "Alistair Darling has never run a campaign.
"He is comatose most of the time."
A Tory parliamentary figure was quoted saying Darling was "useless", adding: "He's not a very good communicator."
Various senior Labour figures are refusing to campaign for Better Together due to the Tory link.
These individuals are campaigning against independence inside the United With Labour group.
Keen was called to the Bar in 1980 and became a QC 13 years later. In 2000, he led the defence of Lamin Fhimah, the Libyan acquitted in the Lockerbie trial. He has also been Dean of the Faculty of Advocates.
Keen said he took up the Tory party job because it was in the "interests of Scotland" for the party to be effectively represented during the constitutional debate.
He said: "We have to be in a position to go out there and represent the fairly large number of constituents who are conservatives with a small 'c' but who don't vote Conservative.
"We need to reconnect with a body of people who have drifted from the party and view the SNP as an alternative vote."
SNP MSP Kenneth Gibson said: "The No campaign's poor start to the year has clearly only exacerbated the growing splits in their camp.
"If even Alistair Darling's Tory partners in the anti-independence campaign are unimpressed with his approach, it's no wonder that the ludicrous scare stories from Project Fear are failing to gain any traction with the people of Scotland."
A Better Together campaign insider said: "We totally refute any suggestion Alistair is doing anything other than a first-class job."
A spokesman for the Scottish Conservatives said: "The Scottish Conservatives are full participants in the Better Together campaign, and believe Alistair Darling is the right man to lead it."
Keen did not return calls.