She said: "The council elections showed people are turning away from the SNP, because they are fed up with the Nationalists' attempt to force another divisive referendum".
Over one in ten votes on Thursday were cast for independent candidates - in the Highlands and the Islands in particular, council elections are often still genuinely local rather than partisan battles.
Ms Davidson also went on to criticise Labour, who slumped to become the third largest party in Scotland's councils, adding: "As for Labour, they were left to count the cost of decades of complacency, arrogance and a failure to respond to the concerns of ordinary families".
An SNP spokesman said: "The arrogant Tories can spin as much as they like, but the fact stands that the SNP won the election last week on a platform of protecting local services while Ruth Davidson's party obsessed over the constitution and were roundly beaten".
"The people have their say at the ballot box and I think the north-east of Scotland has a way of bringing people who make vainglorious boasts down to earth with a sharp bump". "They claim that Glasgow was a Yes city, today they have said "no thanks" to the SNP".
Meanwhile, the SNP have not had any difficulty increasing their vote in local by-elections during the last two years; on average the party's share of the vote has been up ten points on 2012 in such contests.
Browns' top pick Garrett gets sacked by Hall of Famer
Garrett, though, is hoping to be the start of something great with the Browns, but he also wants to temper expectations. Just to correct, he didn't say he'd hurt Ben, he did say he'd take him down, but you have to spend time with him.
Pollsters got the result of the 2015 election badly wrong, concluding that they had underestimated support for the Conservatives and had over-represented Labour supporters in their surveys.
While the constituency boundaries for Westminster are slightly different, the Scottish Conservatives are keen to capitalise on the rise in support locally as the general election approaches.
Mr Rowley stressed: "The SNP failed to win a single majority anywhere in Scotland, and the nature of the voting system means that cross-party deals may be agreed".
Labour leader Jeremy Corbyn said his party faced a challenge on a "historic scale" to win back power, but insisted he could close the gap on the Tories.
"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".
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I only own one Echo, an Echo Dot, but she told me that if I had multiple Echo units, the process would be the same. Similarly, instead of "Alexa, call Mom for Mother's Day", you can ask Alexa to video call Mom for Mother's Day.
However, First Minister Nicola Sturgeon has said only the SNP can "stand up to the Tories".
The party polled 4.1% of first preference votes, an increase on the last election.
"We are in the mix or ahead of the game in the Borders, Dumfries and Galloway, bits of Ayrshire, in Renfrewshire, Edinburgh, Perthshire, Stirlingshire, Angus, right the way up to Banffshire, Aberdeenshire and across to Moray".
As a result, it could well face a particularly strong challenge from the Conservatives in such key seats as Moray, now held by Angus Robertson, and in Perth and North Perthshire, where the incumbent is Pete Wishart.
Of course, these losses of support in the north-east were counterbalanced by gains elsewhere.
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 nearly 40 years.
Holmes, Stanley lead Players after 54 holes, Garcia four back
Holmes (70) hit his tee shot at No. 17 to within 5 feet and Stanley (72) followed with an even closer strike, to less than 3 feet. The Northern Irishman made the ideal start with a birdie on the first, but the four-time major victor then bogeyed the fifth.