The First Minister and SNP admitted the Conservatives in Scotland had “a good day by their standards”, with the party returning a record number of councillors north of the border.
But she insisted the SNP had “won this election comfortably” with her party ending up with “more votes, more seats, more councils where we are the largest party, not just compared to every other party but compared to five years ago”.
Ms Sturgeon said: “Yes, the Tories made gains and had a good performance by their standards - but that support came from Labour not the SNP, so Labour and the Tories are fighting it out for second place while the SNP continues to be comfortably in first place.”
She said: “This was a council election that the SNP fought on local issues, which is probably why the SNP won the election so emphatically.
“But let’s take the Tory argument at face value. They chose to fight the election on the issue of an independence referendum, they talked about nothing else, they didn’t have any policies for local government.
“So they put that issue centre stage and they lost the election. They came second in the election and the SNP came first.
“If you’re going to put a single issue at the centre of your own campaign, then you lose the election, then you’re left with a bit of egg on your face and I think the Tories have egg on their face on that question this morning.
“They’ve had a good day by their standards but we’ve got to put into context - the Tories polled a lower share of the vote in Scotland than Jeremy Corbyn did in England so, yes, a good performance from a low starting point but it’s
Labour that the Tories have taken support from, not the SNP.”
She spoke out after Scottish Conservatives won a record 276 councillors north of the border - more than double the 115 they secured five years ago - with Tories elected in places such as Paisley’s Ferguslie Park, the most deprived part of Scotland
The SNP remains the largest party in local government with 431 councillors voted in, up slightly from its total of 425 in 2012.
But if voting patterns are similar at the General Election on June 8, a surge in Conservative support could see Ruth Davidson’s party oust some SNP MPs from Westminster.
Meanwhile, Labour slumped to become the third largest party in Scotland’s councils, and was kicked out of power in its Glasgow heartland for the first time in almost 40 years.
Ms Davidson said the results showed “only the Scottish Conservatives have the strength to fight back against the SNP”.
She said: “We will speak up for the millions of Scots who have had enough of the uncertainty and division of the last few years.
“We will stand up for everyone who doesn’t want a second referendum on independence.”
Scottish Labour leader Kezia Dugdale also said there had been a “clear backlash against the SNP’s plans for a divisive second independence referendum”.
However, Ms Sturgeon said: “I’ve heard lots of ludicrous arguments in my time in politics but this takes the prize for the most ludicrous argument.”