The First Minister said colleges received more cash this year than last, despite official figures showing a steep fall.
His assertion at First Minister's Questions effectively silenced efforts by Scottish Labour leader Johann Lamont to press him on the further education crisis.
However, minutes after their exchange at Holyrood it emerged he had used a misleading figure to present this year's cash allocation as an increase.
Mr Salmond's embarrassment was heightened by him insisting to Ms Lamont he had provided "as exact an answer as anyone has ever given to Parliament".
He was flanked by Education Secretary Michael Russell and Finance Secretary John Swinney, who nodded agreement.
The First Minister had to return to Parliament to apologise to MSPs at the end of the day's proceedings.
He said: "The figure I used was provided to me and used in good faith. There was no intention to mislead. I take full responsibility for what I say in this chamber, therefore I have taken the earliest opportunity to correct the figure. I apologise to the chamber for this error."
Ms Lamont dismissed the apology and insisted the error was deliberate. She said: "He did not accidentally go from one column to another. The contempt Alex Salmond shows to the Scottish people and this Parliament is breathtaking.
"Facts come second to put-downs and the interests of the Scottish people come second to the interests of Alex Salmond's career. After the European debacle, how can we ever believe a word Alex Salmond says again?"
Mr Salmond had claimed college funding rose from £545 million in the financial year 2011/12 to £546m in 2012/13, adding that this was "by definition an increase in funding".
However, the amount he gave for 2011/12 was a baseline figure and did not include extra spending on bursaries and extra places added during the year.
According to official Scottish Government figures presented to Parliament by Mr Russell in October, the true figure for 2011/12 was £556m.
The figures were accompanied by a note saying "college resource funding has fallen slightly between 2011/12 and 2012/13".
The deep cuts facing further education colleges have been widely reported in recent months. An Audit Scotland report showed funding was being slashed by 24% over three years.
Mr Salmond's spokesman claimed he had been reading from a briefing note prepared by education department staff. Officials then spent four hours checking their figures on college spending before Mr Salmond returned to the Holyrood chamber just before 5pm.
In his apology, the First Minister acknowledged he had ignored budget changes.
The Education Secretary was also ordered to apologise in writing for relying on the same erroneous figure in a parliamentary answer on June 28.
Mr Salmond's apology came three weeks after he agreed to an inquiry into allegations he lied in a TV interview about Government legal advice on an independent Scotland's membership of the EU. He denied lying.
And, in October last year, Mr Salmond was forced to correct his interpretation of the views of Dr Matt Qvortup, a constitutional expert, on the referendum plan.
He claimed Dr Qvortrup had endorsed the SNP Government's plans for a two-question vote but the First Minister later admitted to Parliament the information he used had been "wrong".
Hugh Henry, Scottish Labour's education spokesman, said later: "It is beyond belief the First Minister thought college funding was going up when he is cutting it."
A Scottish Conservative finance spokesman said: "If you play fast and loose with figures you are bound to get caught out eventually. Too often the First Minister puts bombast, bluster and boastfulness before accuracy and clarity."
A Liberal Democrat education spokesman said: "We have discovered that the stronger the assertions from ministers that they are absolutely right, the more likely those numbers are to be wholly wrong."