With more than 70 per cent of the ballots counted on Monday, the Liberal National Party's primary vote has slumped 4.7 per cent to 39 per cent, while Labor's has edged up one per cent to 27.8 per cent.
Ms Palaszczuk says the dip in major party support shows Queensland voters want politicians to work together rather than fight.
"The public is sick and tired of the adversarial nature that comes from the two major parties and they want a government that looks after them and their families," she told reporters on Monday.
"They actually want people to understand their issues, be in touch with their issues, and they're the people who will get elected, so it's a lesson for everybody in politics."
One Nation suffered a 1.3 per cent dip in first preferences pushing their primary to 7.6 per cent, while Clive Palmer's United Australia Party edged up 1.7 per cent swing to 5.2 per cent.
However, the Greens' primary vote rose 2.5 per cent to 12.8 per cent with the party winning one seat from Labor and possibly two from the LNP in inner-Brisbane.
Ms Palaszczuk said the swing showed the community wanted stronger action to mitigate climate change.
"Unfortunately the former federal government did not embrace what the community was talking about, thinking and saying, and hopefully now we will have more dialogue in our media outlets as well," she said.
As for the Liberal Nationals, re-elected Gold Coast MP Angie Bell disagrees with suggestions the coalition must shift further to the right to maintain its base.
"Now is the time for political realignment to the middle ground where there is a medium for all Australians to prosper, grow and live harmoniously together," Ms Bell said in a statement.
Meanwhile, Ms Palaszczuk insisted her government had the right policies when asked about growing support for the Greens.
"We have a very progressive environment agenda, and we have a very progressive jobs agenda," the premier said.
"We are growing the economy, we recognise that we have traditional industries, and we have emerging new industries, and my government will always focus on jobs"
However, she indicated she had no plan to increase her target of cutting emissions by 30 per cent by 2030.
Ms Palaszczuk welcomed federal Treasurer Jim Chalmers' willingness for talks on the federal health funding model after she had campaigned for months for a 50-50 split with states.
"We want to work with the premiers of both political persuasions to get great outcomes for people, but no doubt there'll be lots of conversations about that in due course," Mr Chalmers told ABC Radio on Monday.
The premier said she was looking forward to raising health funding at Prime Minister Anthony Albanese's first national cabinet.
"The former prime minister would not even allow it to be on the agenda to be discussed," she added.
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