The Maritime Union of Australia wants seats at West Australian Premier-elect Mark McGowan's cabinet table for trade unions, in return for what it sees as a key role in winning the state election for Labor.

Maritime Union state secretary Chris Cain said Mr McGowan owed unions for their support and needed to deliver on his anti-privatisation election promises and push for Australian jobs.

Outgoing Premier Colin Barnett had persistently warned a McGowan government would be controlled by the unions and by former unionists who pepper the ranks of Labor MPs and likely ministers.

But Mr McGowan today sought to hose down any perception he was beholden to unions, saying his Government would make decisions in the best interests of the state.

Mr Cain said Mr McGowan was "independent" but he understood the central role unions played in the victory.

"We've delivered for them so it's not too much to expect them to deliver for working-class people," he said.

Asked if he thought the Premier-elect owed unions some cabinet seats he said: "Yes, I think he does."

"When I say he owes us, I'm saying I'm part of the public as well as a unionist, but he owes the trade union movement because collectively together ... our members are very, very disciplined," Mr Cain said.

"I've got to say I went to a meeting a month ago and there was 200 volunteers going on the polling booths all around the state."

The Electrical Trades Union (ETU) also credited its campaign with the Australian Services Union against the sale of state electricity utility Western Power as a key driver in Labor's success.

WA Premier-elect Mark McGowan said the party won the election under its own steam. ( ABC News: Jacob Kagi )

Mr McGowan does not see it the same way.

"No, the party won the election, and the hard work of the party and its supporters," he told 6PR radio.

"And I appreciated the assistance of union volunteers and union campaigns in relation to the campaign, but I think the people of Western Australia voted in favour of the platform that WA Labor put forward.

"You'll see that I always act in the public interest and I think with the result that's occurred is a mandate for what I've had to say, and that is I'll act in the public interest, I'll always act ethically and we'll make decisions based on what's right for the future of the state."