The Gotham villagers were desperately trying to get sandbags to stop their homes from flooding, but the advisor said he could only find a "Gotham City in New York" on his system.
Rushcliffe Borough Council, in Nottinghamshire, has since apologised.
It said the calls were answered by someone outside of the area.
"He said the only Gotham he could find is Gotham City in New York," said Racheal Webster, one of the residents who phoned up.
"I said 'are you trying to be funny? Is that some kind of joke?' and he said 'no, that's the only Gotham I can find'."
The conversation became "quite heated" when he said he could not help her, she said.
"I said 'well we do exist, obviously, we are getting flooded, the water is starting to come in'," she said.
"He said the same thing to my neighbour when my neighbour called as well."
There is no such city as Gotham in the real world, but New York is sometimes referred to as Gotham, and the nickname stems from the Nottinghamshire village of the same name.
Read more: The real Gotham - The village behind the Batman stories
The villagers phoned a local emergency number printed on the council's website when flooding began in Gotham on Wednesday evening.
However, the council said its out-of-hours service is provided by a national company.
David Banks, executive manager for neighbourhoods, said: "Unfortunately, the advisor Mrs Webster spoke to wasn't familiar with the area and wasn't able to locate Gotham on the system to log the call.
"He tried to help by doing a Google search of 'Gotham' which returned results referring to the Gotham in America.
"We understand that experiencing flooding is stressful and upsetting and we are working with our out-of-hours provider to ensure that this doesn't happen again."
Residents living in a village sharing its name with Batman's city of Gotham were told their address did not exist when they phoned the local council.