Steve Tulley said that last week's poll had effectively been a "second referendum".
It comes seven months after Coun Tulley, who voted in favour of Leave at the 2016 referendum, claimed Ms Cooper, the Labour MP for Normanton, Pontefract and Castleford, "wouldn't know democracy if it scratched her in the eyeballs" in a slight at her Brexit stance.
His fresh criticisms were made as Wakefield councillors reflected on the election result, at their last meeting in 2019 on Wednesday.
The Wakefield constituency elected a Conservative MP for the first time since the 1930s last week, as Mary Creagh, who's also been criticised for her position on the referendum, lost her seat.
Ms Cooper retained hers with a reduced majority, as did Labour's Hemsworth MP John Trickett, but the party had a disaster nationally, losing swathes of seats in their traditional heartlands in the north and Midlands.
Many commentators have attributed that result to Jeremy Corbyn's Brexit policy, which was to negotiate a new withdrawal deal from the EU before holding a public vote on it, with an option to Remain.
Coun Tulley said: "I think last week was a lesson that you get what you deserve when you choose to ignore what the people who send us to Parliament, or indeed here, say.
"Last week's General Election was an election in name only. It was a second referendum on Brexit whether you like it or not.
"If you choose to ignore what the people say, the consequences can be dire.
"But I think it's incumbent on this council to make sure Wakefield's new MP has his feet, metaphorically held to the fire, because this council has seen millions and millions of pounds worth of cuts, from which we have all suffered.
The leader of the Conservative opposition group, Nadeem Ahmed, said he believed it was important MPs were "called out" when it was felt they weren't representing the public adequately.
He said: "I think there's a certain disconnect between MPs and their constituents and we've seen that at this election.
"I think it's important, whether privately or publicly, as Coun Tulley has done in the past, that we call these MPs out.
"All of us here suffer at the polling station when they say and do things that are against the wishes of the people, because many people don't know the difference between MPs and councillors."
The new Conservative MP for Wakefield, Imran Ahmad-Khan, will be invited to visit the council to observe its day-to-day operations.
The council's new Labour leader, Denise Jeffery, and Coun Ahmed both pledged to work together for the good of people in the district, though Coun Jeffery clarified there would be "no love in" between the two parties over issues they disagree on.
Describing the election result as "disappointing", Coun Jeffery added: "Going forward as a council we need to listen, focus and act, and with my new deputy leader and myself that is what will happen."
Local Democracy Reporting Service