Party elder statesman Gordon Wilson accused ministers of being out of touch with electors and suggested they should "get out more" if they are going to strike back against the Labour Party.
Wilson, Salmond's predecessor, who headed the SNP between 1979 and 1990, said the party's high command were being side-tracked by their day-to-day work at the Scottish Parliament.
"Having been in parliament you tend to associate politics with the parliament. Politics is on the street and perhaps they ought to get out more," he said.
Wilson's open dissent reveals the depth of dismay in the party in the wake of the SNP's crushing defeat last week. In particular activists are angry at decisions perceived to be anti-Glasgow – including the scrapping of the Glasgow Airport rail link – which they think played a major part in the SNP candidate's failure.
Although Glasgow North East is Labour's safest Westminster seat, the scale of the loss – Labour polled three times as many votes as the Nationalists – was a major surprise.
The defeat undermines the credibility of Salmond's prediction that the SNP can win 20 Westminster seats at the general election next year.
Wilson's criticism shows open division within the party for the first time in recent years. Wilson added that the SNP high command had been too slow to pin the blame for public sector cutbacks on the Labour government.
"They need to repeat the message again and again and again until they are sick of it," he said. "Around about nine months ago, the SNP should have led the attack on Labour on the budget cuts. It should have railed about how Britain is bankrupt."
He added: "On the Glasgow Airport rail link, we should have turned around to (Scottish Labour leader] Iain Gray and said, 'Yes, you have a good point about it, so why don't you get on to Alistair Darling and ask him for 300 million more?'"
Wilson is a respected figure in Nationalist circles. At the SNP annual conference last month he gave the keynote Donaldson Lecture, in which he argued that "negative campaigning" must have its place in the SNP armoury,
His call comes as the recriminations within the SNP camp over the loss continued this weekend.
One well-placed source said: "They (the leadership] need to recognise the real world isn't Holyrood. There is an arrogance there. We are up against some clever people."
In the wake of the loss, deputy leader Nicola Sturgeon acknowledged the SNP had been caught off-guard by Labour, admitting it needed to rebut attacks on its record "earlier and more effectively".
But Labour continued to press home its advantage following the result. Scottish Secretary Jim Murphy said the SNP's prediction of winning 20 seats at the general election was "a fantasy beyond fiction".
He said: "The SNP will be lucky to keep what they have got. They are a party that has lost its way."
On Wilson's comments, a spokesman for the SNP said last night: "We will learn the lessons. The constituency had been Labour for nearly 75 years so it was always going to be difficult for us to change that."
He added: "The Scottish Government remains very popular and is polling significantly more than we were getting at the election in 2007 despite being mid-term."
It is understood new campaigning technology tried by Labour for the first time in the Glasgow North East will be used across all marginal seats in the UK general election. Party chiefs were able to monitor exactly which of their known supporters had voted, allowing them to rally those who hadn't.
Meanwhile, Strathclyde police are continuing to examine three ballot papers from the St Dennis polling station amid allegations of duplicate voting.
The case has been passed onto the Strathclyde Police Fraud Squad.
• Reality check for SNP: Eddie Barnes on the Glasgow North East by-election