The First Minister said special adviser Campbell Gunn made a "mistake and a misjudgment" when he e-mailed a journalist about Clare Lally, 33, who played a leading role at a Better Together rally.
Mr Gunn was ordered to apologise after pointing out Ms Lally - who introduced herself at Monday's event as "just an ordinary mum from Clydebank" - was a member of Scottish Labour's shadow cabinet.
He also mistakenly claimed she was the daughter-in-law of former Glasgow Lord Provost Pat Lally.
The e-mail prompted claims Mr Gunn, a former political editor of the Sunday Post, was attempting to undermine her and portray her as untrustworthy, sparking calls for the First Minister to sack him.
But challenged at First Minister's Questions yesterday, Mr Salmond insisted the apology - which was not accepted by Ms Lally - was the right way to deal with the blunder.
Responding to questions from Scottish Labour leader Johann Lamont, he admitted Mr Gunn made a mistake by claiming she was related to Pat Lally.
The First Minister added: "The misjudgment is believing that drawing attention in an e-mail to someone's Labour Party connections, whether it is that they are a member of the shadow cabinet or any other connection, was appropriate to do."
Later, questioned by Scottish Tories' leader Ruth Davidson, Mr Salmond stressed: "Campbell Gunn was not disseminating inappropriate material in terms of the special advisers' code of conduct.
"It was a misjudgment and a mistake, for which he has comprehensively apologised."
His comments came amid fresh calls for Mr Gunn to be sacked for breaching the code of conduct that governs the behaviour of special advisers.
The rules expressly forbid the "dissemination of inappropriate material or personal attacks" and say any adviser found to be in breach "will automatically be dismissed".
The Conservatives, Labour and Liberal Democrats all said Mr Gunn should be sacked for breaching the code.
Asked after First Minister's Questions whether Mr Gunn's actions were appropriate, Mr Salmond's chief political spokesman replied: "Clearly not".
But he strenuously denied Mr Gunn had been responsible for internet abuse aimed at Ms Lally after she addressed the Better Together rally.
The issue of internet abuse also flared up yesterday following the decision by author JK Rowling to donate £1m to the Better Together campaign, which led to her being heavily criticised on social media.
A Holyrood motion tabled by Scots Tory chief whip John Lamont yesterday called for "an end to personal attacks against all people in Scotland who choose to express a view in the independence referendum".
It also called for campaigners to consider "Scotland's reputation as a tolerant, peaceful nation" and said "a vigorous, strong and passionate debate can be held between the No and Yes sides without descending into personal abuse".
MSPs were also invited to condemn the "disgraceful abuse" directed at JK Rowling and Clare Lally "solely for expressing their own sincerely held beliefs about the best way forward for the nation". Last night the motion had been backed by 33 MSPs, all from the Labour, Conservative and LibDems' ranks.
Speaking during FMQs, Mr Salmond made a separate call to end the online abuse.
He said: "All of us, every single one of us, should condemn abuse on the internet.
"Every single one of us should condemn that handful of mindless idiots who engage in such things in the early hours of the morning."
He added: "We should as a Parliament and as a society stand up against that handful of people who are attempting to pollute this independence debate."