"They're individual contests being fought in very differing situations, from local council-level, issue-driven campaigns up to large mayoral fights with some well-known politicians", a Labour party spokesperson said.
Despite notable Tory success in the Scottish council elections, the huge SNP leads in parliamentary seats protect Nicola Sturgeon against losses, the analysis said.
The Conservative party have taken control of Warwickshire County Council, winning 36 of the 57 available seats.
Labour finance spokesman John McDonnell acknowledged the party had suffered a tough night, but told ITV that the results were not "the wipeout that people expected" and insisted it is still "all to play for" in the national vote.
Labour's local results do seem to confirm fears some in the party have shared privately: The party is more confident of holding on in the South, but is anxious about a collapse in its vote in the North.
Liberal Democrats increased their number by one and Labour lost two, with Ukip losing the lot.
Theresa May's hopes of a General Election victory on June 8 have been boosted after local contests showed Labour suffering losses and the Ukip vote collapsing.
"Former Liberal Democrat voters are coming back, I think there is some evidence - because of Jeremy Corbyn's very feeble leadership - we are seeing Labour voters coming over to us as well". "We knew it was going to be a hard night".More news: Not yet freedom for Assange, faces arrest in Britain
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By the 2010 General Election, Labour, under Gordon Brown, had been able to regain lost ground, securing 30% of the vote compared to Cameron's Tories on 37% and the Lib Dems on 24%.
It was a triumphant election for the Conservatives, pointing to a landslide victory for Theresa May in next month's general election.
By the time Britain woke up on Friday morning, only a fraction of its local election results had been counted but the outcome for each of the political parties was already clear.
At 1000 GMT and with more than a quarter of the 88 local authorities declared, the Conservatives had control of 636 seats, a net gain of 179.
Voters across England, Scotland and Wales went to the polls Thursday to choose almost 5,000 new local councilors, in the shadow of campaigning for the snap June 8 general election and a bitter debate over Britain's departure from the European Union.
TV pundits made projections from the local votes to next month's general elections, estimating a Conservative majority of 48 seats in the House of Commons - well above the 330 seats in the last parliament, which had given the party a working government majority of just 17 seats.
Too many fantastic councillors, who work tirelessly for their communities, lost their seats.
UKIP's Mr Howson said he was "gutted" with the results. The party even lost control of the city council in Glasgow, Scotland's biggest city and once the staunchest of Labour strongholds.