With an air of inevitability that Atlanta will eventually build a new stadium to replace the Georgia Dome, residents in the neighborhoods near the proposed site pressed City Council members Wednesday to have their backs in the final negotiations.

One after another, speakers from Vine City, English Avenue and Castleberry Hill pleaded with leaders to push for everything from noise buffers to economic aid in any deal that gives the Atlanta Falcons a new $1 billion playing field, part of which will be paid for with public funds.

“If a stadium is built, we only get one chance to do it right,” Scott Chapman, president of the Castleberry Hill Neighborhood Association, said in asking that the communities also have a seat at the table during the negotiations. “There are no do-overs for billion-dollar mistakes.”

Said the Rev. Darrion Fletcher of Vine City, “We are tired of people stuffing things down our throats as if we don’t exist.” He demanded that the community be involved in the process. “We feel like our voices have not been heard.”

The discussion was the latest public hearing the City Council has held since Gov. Nathan Deal and Mayor Kasim Reed took over talks between the Falcons and the state in January. Residents and leaders packed a standing-room-only hearing last week that gave many their first chance to give input on the project.

The team has said it wants to play in a new stadium by 2017, when its lease at the Georgia Dome is likely to expire. The Falcons began negotiations more than two years ago with the Georgia World Congress Center Authority, on whose land the facility would be constructed, to use $300 million in hotel-motel taxes in a public-private partnership.

But those talks ran into trouble late last year after it became clear the Legislature, which would have to approve raising the GWCCA’s borrowing limit, did not favor using public funds. The governor stepped in in January to lower the hotel-motel contribution to $200 million and use Invest Atlanta, the city’s economic development arm, as the bonding authority.

Wednesday’s hearing was much more subdued than the previous outing. While a few said Falcons owner Arthur Blank had the financial means to do the project himself, most either supported it or implored council members to be cautious in signing on the dotted line.

In a surprise visit, former Mayor Andrew Young was one of the first to speak Wednesday about the proposal. Young, who backs the new stadium, said there have always been naysayers about expensive projects.

“Everything that has happened in this town has been controversial,” he said. “We just barely carried MARTA. Even when the airport was built and I talked to Delta (Air Lines) about the T-terminal as a new international terminal, they told me we didn’t need it. They even got someone to do a survey, a feasibility study that showed that it wouldn’t work.”