Labour remain the biggest party on Bridgend council, with 26 seats, but the Conservatives, who only had one seat, now have 11.
Ballots were counted Friday from contests for local councils in Scotland, Wales and many parts of England, as well as from mayoral competitions in several cities.
Nuttall claimed the party, which did well in 2013 council elections and won 3.8 million votes in the 2015 general election, was a “victim of its own success”.
But another defeated Labour council candidate, Phil Johnson – who is Labour’s general election candidate for Nuneaton- told the BBC: “People have been saying to us that Jeremy Corbyn’s style has been putting them off voting Labour”.
But he said he was disappointed that “local issues had been drowned out” because of the calling of a general election and smaller parties had paid a price, handing the Conservatives a “healthy majority”, which he described as “bad news for Norfolk“. “But we, the whole Labour movement and the British people, can’t afford not to seize our moment”, he said in a statement.
Corbyn said that in spite of the results of the local elections, the general election represented “an opportunity” and a “chance to break free” from what he termed “a system that is rigged for the rich”.
With 31 of 34 results in, the Conservatives had an extra 307 councillors in England and control of another 10 local authorities.
With the Conservatives and the opposition tied on 33 seats each, the battle came down to the 67th and final seat. “We knew it was going to be a hard night”.
“Looking across the board it’s got to be seen I think as a pretty solid result for Plaid Cymru and bodes well for the poll which is coming up in just a few week’s time”. “We’ve now got five weeks to get a message out there”.
“There’s no question the Tory vote is on the increase and therefore we have to galvanise the SNP support”, he told Press Association Scotland.
The Liberal Democrats increased their share of the vote by 7%, but lost almost 40 seats in total. But Labor held seven councils including Cardiff, Swansea and Newport.
And it was a disastrous day for the anti-EU, anti-immigration UK Independence Party, which lost all 114 seats it was defending, and won only one new one.
Nuttall claimed that, if his party’s hammering was down to a Tory advance driven by May’s determination to leave the European Union, then it was a price he was “prepared to pay”.
Some 52% of Labour voters who have quit the party since the last election said they would return if Mr Corbyn stood down as leader.
Political analysts have argued that Ukip had become a “gateway drug” for voters in Labor heartlands to shift to the Tories, which could be hugely damaging for Corbyn’s party.
The party’s vote was squeezed in Brexit-supporting parts of the country, limiting gains.
The divisions in the Labour ranks were underlined when former shadow home secretary Andy Burnham – the party’s newly-elected metro mayor for Manchester – failed to show up for a visit to the city by Mr Corbyn to celebrate his triumph.