Liverpool City Council used a online budget simulator to ask residents about a proposed council tax rise of 5%, plus a further 6% to pay for social care.
Joe Anderson said the plan would not go ahead after 57% of respondents said no.
He also revealed plans for a Liverpool lottery in his New Year message on his Liverpool Express blog.
He said following the "feedback... I will not be proposing to hold a referendum on any additional increase beyond the 4.99% limit set by government".
Work was continuing on the full details of the authority's budget, he said, which would then undergo consultation in 2017.
He added that he was "surprised and proud that so many, 43%, said yes".
"It's a truly heart-warming reminder of how caring our city really is," he said.
Green party leader Councillor Tom Crone said the consultation was a "sham exercise".
"The weak consultation was never going to secure support for a tax rise," he said.
He said the mayor's decision not to hold a referendum meant there would be "tens of millions of pounds more cuts to services in the coming years".
Liberal Democrat leader Councillor Richard Kemp, said: "The public were never going to buy it over concern about the waste of existing council tax income."
Mr Anderson said the Liverpool lottery card would help local causes, adding that more details of it would be revealed in the coming months.
"Liverpool people are amongst the most generous in the country and I believe will support the initiative to help us cope with the growing numbers of people dependent on us," he said.
Councillor Kemp said his party would oppose the lottery idea.
He said: "The overwhelming evidence is that existing lottery users are already from the most deprived parts of the community.
"A new Liverpool lottery will be a tax on the poor to pay for services to the poor."
There will not be a referendum on an additional council tax rise in Liverpool after the results of an online poll, the city's mayor has said.