The party yesterday demanded an explanation after the broadcaster appeared to offer a personal view that an independent Scotland would find it "quite hard to get back in" to the EU.
Stewart Maxwell, a senior Nationalist MSP, also complained that Mr Marr may have broken the corporation editorial guidelines during heated exchanges with the First Minister on his Sunday morning show.
Pete Wishart, the SNP MP and culture spokesman, said on Twitter there would be "consequences" for Mr Marr, as other Nationalist campaigners took to the internet to accuse the corporation of bias. A number said they would be making formal complaints to the BBC.
The row erupted as Mr Salmond was quizzed about the SNP's claim that an independent Scotland would be fast-tracked into the European Union on the same terms of membership as the UK.
Last month, during an unexpected appearance on the Andrew Marr show, European Commission president Jose Manuel Barroso said he believed it would be nearly impossible for an independent Scotland to join smoothly and compared the country's situation with that of Kosovo, which has not been recognised as a state by Spain.
During yesterday's interview Mr Marr told Mr Salmond he had been "quite surprised by how incredibly steely and sure" Mr Barroso had been.
He said: "He was absolutely adamant in private and in public on the sofa that it would not happen and he said he was speaking for many other big European heads. I wonder why you regard this as yet more unionist bluster - he had no particular dog in this fight."
Mr Salmond replied: "I think perhaps he has", and repeated claims Mr Barroso's remarks were part of a campaign to become Secretary General of Nato and that he "was sucking up to London in order to advance that process".
As the exchange continued, Mr Marr said: "I think it would be quite hard to get back in, I have to say."
The host tried to move on to another question but an angry Mr Salmond pulled him up for providing an "Andrew Marr analysis".
Challenging the broadcaster, he said: "Is that an individual expression or is that an expression of the BBC?"
Mr Marr said: "No it's not. I've got no views on this, nor does the BBC."
Last night SNP MSP Stewart Maxwell said: "There are questions for the BBC to answer over their coverage of this issue. Firstly, they failed to press President Barroso about his comparison of Scotland - which has been part of the EU for over 40 years - with Kosovo.
"And now a presenter offers what appears to be a personal view on an independent Scotland's EU membership. The comments from Andrew Marr appear to be outside the BBC's editorial guidelines, and no amount of backtracking can change that."
A spokeswoman for the First Minister said: "Though the specific comment made was surprising, the First Minister responded at the time and we do not intend to complain about a programme we were represented on. The BBC face a more generic issue in relation to referendum coverage that has been highlighted by independent academic research, and it is for the BBC to explain their overall approach."
In a separate interview on the same programme yesterday, Shadow Chancellor Ed Balls insisted a currency union between an independent Scotland and the rest of the UK would be the "euro crisis in spades" as he and George Osborne again joined forces to make clear that any future Westminster Government would not sign up to one.
Mr Salmond said the warning was part of a "long litany of scaremongering". He insisted the claimed "moral superiority" of holding the consensual Scottish referendum, compared to the snap one in Crimea, would "dissolve in a puff of dust" if the Edinburgh Agreement was not adhered to.
The First Minister said the SNP Government's appointed Fiscal Commission had come up with a "Plan B, C, D, E and F" but that he and his colleagues would argue for the best option; a shared sterling zone.
When questioned on the show, Mr Osborne insisted sharing sterling was now off the table, saying: "You would have to ask yourself, if you tried to create a currency union, would you not need much more control over the Scottish budget, would you not need to stand behind Scotland's banks?
"When you start to ask questions about how that would work, you come to see it would not be in the interests of the rest of the UK and I don't think it would work for Scotland either."
Last night a BBC spokeswoman said: "Andrew himself made it clear on air that he had not been intending to express a personal opinion or that of the BBC, but was simply putting forward an argument from President Barroso who, as European Commission President, has an integral insight within the debate.
"The BBC's coverage of the Scottish Referendum debate has been fair and balanced and we will continue to report on the story without fear or favour."