Proposals to introduce public question time sessions at Wakefield Council meetings have been voted down.
Liberal Democrat councillor Tom Gordon said the local authority was "silencing people when trust in politics was at its lowest" by not allowing people to quiz senior councillors.
But the idea was rejected by the ruling Labour group, who said some members of the public may be "intimidated" by the prospect of speaking at public meetings.
Presenting a motion on the issue at a full council meeting on Wednesday, Coun Gordon said: "It would allow local taxpayers to come here and hold us to account all the year round.
"Other councils in the area have similar things in place.
"If people vote against this motion today, we're slamming the door in people's faces and saying, 'Don't bother coming because you won't be able to speak'."
Independent member Alex Kear spoke in support of the idea, saying it was a "fantastic opportunity" to make the authority more open and transparent.
The Conservatives agreed, and also suggested that meetings be held across the Wakefield district.
But Labour Cabinet member Matthew Morley said that social media meant elected members were more accessible to the public than ever before.
He said: "This motion is 15 - 20 years too late. It's a bit old hat.
"As a local member we are accountable on our Facebook pages, in our community groups. We have street surgeries. That's how we're held accountable.
"If you're going to get Mrs Jones from Wakefield North coming to see Councillor Morley at this council meeting and asking why the drains outside her house haven't been sorted, I won't know the detail.
"I'll say, "Thanks Mrs Jones, I'll write back to you," and we'll have dragged her all the way here to this council chamber.
"We're better off by residents communicating with their local members."
Councillor Jacquie Williams added: "We can ask questions to officers on behalf of residents anytime, not just once a month. We feed the answer back.
"This motion seems to be reneging on the duties of a local councillor, and asking the public to do it themselves."
Local Democracy Reporting Service