The results of an informal Otago Daily Times online poll showed opposition to the mural, as 62% of 3400 respondents said it was not a good use of ratepayers' money.
Among those to criticise the spending was Cr Aaron Hawkins, who, in a Facebook post, said the "monument to a visiting pop star" was "a bit embarrassing really".
"Particularly when we have our own long and proud creative history worth celebrating."
Ewan McDougall agreed, arguing the money would be better spent on a mural of Ralph Hotere or Dunedin musicians such as The Chills, rather than "someone with no relationship to the city, apart from a concert".
Shirley Walthew said paying for the mural was "met by disbelief from this ratepayer".
The council should spend the money on better roads or improved flood controls, she argued.
"There are far more important things that that sum of money could be spent on rather than a 'pop singer'."
Tom Phillips said the council's decision was "out of order" and the money should be used to make the Octagon more "family-friendly" and vibrant at all times.
New plantings could be added, or school children invited to perform in the Octagon during lunch hours, he said.
In an interview with Television New Zealand's Seven Sharp last night, Sheeran said he could understand why the mural might annoy people.
"I saw they're doing some sort of mural and it's pissing people off," he said. "It's up to them, I'm sure if it was my hometown and I had someone coming that I like I might do the same.
"I'm sure not everyone in New Zealand likes me so of course some people are going to be like 'that's a bad idea'".
However, the singer said he was not letting it get him down.
"The older I get the less I care about people's opinions, I never meet these people and when I do they're always super polite and nice."
