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."

Katie Milby, 13, has Morquio A, a degenerative syndrome which affects about 105 people in the UK.
It leads to the progressive deterioration of mobility, health and stamina.
Her friend Kyle Pirrie has started a petition seeking to see the medicine Vimizim made available on the NHS.
There is no known cure to Morquio syndrome but the drug improves the life of people with the condition.
It replaces a missing enzyme which allows children to continue to grow, as well as improving stamina and the ability to walk. It also relieves pain.
The drug's manufacturers have been providing the treatment to patients at their own expense but they are going to withdraw it unless the NHS in England and Scotland commit to funding it.
The Stranraer Academy student said her life would be markedly different without the drug.
"I wouldn't be able to move I'd just be in so much pain," she said.
"And I probably wouldn't be able to go to school."
It was that situation which prompted her friend to launch the petition which now has nearly 2,000 signatures.
"As a friend I suppose I felt kind of bad that she was going to be denied this because I know she has got a great outlook on life," Kyle explained.
"She's funny, she's friendly and I would hate to see her in pain all the time."
Galloway and West Dumfries MSP Alex Fergusson has also backed the petition.
"This is not a cheap medication but, as Katie herself asked me, how do you put a value on a human life?" he asked.
"There are only just over a hundred sufferers throughout the UK, with just five in Scotland, and those who have had treatment with Vimizim report a massive reduction in pain and the other symptoms of this syndrome.
"Life expectancy, which rarely exceeds the mid 20s without treatment, can be considerably extended with this treatment, and it is enormously to the credit of Katie and her friends that they have raised this petition to try to ensure that the treatment is available to all."
The Scottish Medicines Consortium said the drug was currently going through its assessment process.
It added that a decision on the medicine was expected to be published in early September.
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.
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A Stranraer Academy student has set up a petition to ensure a life-enhancing drug is made available to a fellow pupil with an extremely rare disease.