Labour leader David Cunliffe conceded yesterday that he regretted not campaigning alongside the Greens, who had sought a joint agreement.
He did not believe the parties should merge "but I do think there is potential for us to operate in a more cohesive way".
Ms Turei said Greens and National had worked together before, such as on legalising gay marriage, but the parties had little in common. She reiterated the Greens' wish to sign a cross-party agreement with National on child poverty, despite National's rejection of the proposal during the campaign.
The Greens also had no plans to narrow the party's platform to improve its chances of forming a coalition with centre-right parties.
Under Russel Norman and Ms Turei's co-leadership it has increasingly focused on economic and social justice issues.
Ms Turei said the Greens had always had a wider vision and "will never step back from that".
The party would approach this term as it did the last - with a goal to be the leading Opposition party.
Co-leader Russel Norman said that with National in a position to govern alone and Labour facing a leadership contest, the Greens' role in Opposition was more important than ever. The two leaders said they were not disheartened by the Greens' slight slip in support, but they were clearly a little disappointed yesterday.
The Greens had performed strongly on the cross-benches for three years, and followed that up with a highly organised election campaign with specialised digital and youth strategies, and regular, widely publicised policy launches.
The party attracted some large donations and raised more money than ever before, believed to be well over $1 million.
But after National's win on Saturday, its MPs face another three years outside government and 18 years in total in the wilderness.
Ms Turei said: "This is the nature of elections. You just can't tell what's going to happen. Frankly, it could have been much worse for us this time if we had not run such a good campaign.
"It's a good result in the circumstances where there's been a shift to the right and there's been all this chaos from the Internet Mana and mass surveillance."
The party would bring in one new face into Parliament, Wellington-based James Shaw, and was likely to lose a sitting MP Steffan Browning when the final results came in.