James Kelly, Scottish Labour's general election campaign manager said: "It's clearer now than ever before that only Labour can defeat the SNP in vast swathes of Scotland".
The Conservatives returned 276 councillors north of the border, well over double the tally they secured in the last local government elections five years ago.
Labour candidate, Jo Kirby, announced that she would stand in the June 8 election last week.
He said: "There was no outright victor, the SNP have one more member, and that means we have to have a totally different mind-set".
Party leader Nicola Sturgeon said: "The SNP has won the council elections".
Earlier on Saturday Ms Sturgeon described suggestions as "ludicrous" any claims the surge in Tory support in Scotland could derail her bid to hold a second independence referendum.
So, even if the SNP's performance in the local elections may not necessarily signal a sharp decline in the party's prospects for June's general election across Scotland as a whole, it does look as though the party's position has weakened significantly in the north east.
"In seats like Rutherglen and Hamilton West, and in most areas across Scotland, it's a two horse race between Labour and the SNP".
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Goode's perfectly weighted grubber was pounced upon by the 30-year-old, who ran in to bring up a landmark score. Saracens marched down the other end and Farrell scored a penalty to seal the victory.
"In standing up to the SNP's drive for separation, she is now more in touch with Scotland than Nicola Sturgeon". It also went from first to second place in Aberdeenshire.
What was no more than a one-point lead over Labour in the local ballot boxes had seemed like small beer after the SNP's success in winning an overall majority at Holyrood a year earlier.
That compares to the 394 seats the party won in 2012. It would be nice to believe that Thursday's election was a series of local referendums on local services rendered (or not), but it would be a fantasy: this was a national election fought on national issues, and those issues revolved around the prospect of another independence referendum.
The Conservatives are bidding to oust a number of high-profile nationalists, including Westminster leader Angus Robertson, former first minister Alex Salmond, and Pete Wishart, the chair of the Scottish Affairs Committee, in the General Election.
Preliminary talks are understood to have taken place with all four authorities at senior official level, and the new SNP leader of Scotland's biggest council, Glasgow, says today in an article in a Glasgow local newspaper: "We want to rejoin COSLA, pretty much straight away".
Labour's former council leader Frank McAveety, who retained his seat in Shettleston, said: "The SNP predicted they could return 56 councillors, they've only returned 39 councillors".
"I think this (General Election) has the possibility to reshape not just the electoral map of Scotland, but the politics of Scotland and the framework of the question of constitution in Scotland.it's that important". Labour shed 112 councillors to trail in third on 262, losing control of three councils. And the SNP have not had any difficulty increasing their vote in local by-elections during the last two years.