While the National Party was a "behemoth" of money and strategists, he said, the Green Party's strength came from its members.
"If we're going to contend with such a formidable adversary, we need a lot more of them. And then twice that number again."
Secondly, Mr Shaw said, the Green Party needed to be more like modern New Zealand.
"People vote for people they feel a connection to. If we aim to govern the country then we need to represent it."
That meant recruiting more Maori, Pacific Island and Asian candidates, and more farmers, businesspeople, doctors and lawyers, he said.
"More of almost everyone. Although, National can keep their tobacco lobbyists."
Mr Shaw, who helped Greens win more party votes than Labour in Wellington Central, also wanted to modernise the party's campaigns.
"Technology-based, data-driven but founded on communities, self-organisation, and on the passion of volunteers. This type of campaigning is perfect for the Green Party. "We used it in Wellington Central last year. We need to use it in every electorate in the country in 2017."
The new co-leader made it clear on the campaign trail he did not want to form a Government with National. But he was open to working with National on common causes, in particular climate change.
"We should talk to each other rather than past each other, and agree on an ambitious [emissions reduction] target that New Zealanders can be proud of.
"New Zealanders want their politicians to work together, and act on common interest. Let's find common interest on climate change.
That is my challenge to John Key today."
Mr Shaw said New Zealand's cities and regions were transforming in radical ways and at "terrifying rates". One of the party's key aims under his co-leadership would be to "stop this radical change".
His speech coincided with the launch of a new climate change campaign by the party, which urged Government to adopt measures which would help keep global warming to less than 2C.
Mr Shaw tackled some of the criticisms levelled at him and at the Greens since the election.
He indicated that the party would not focus more narrowly on environmental issues, saying social and environmental issues were inextricably bound together.
"Some economists and commentators tell us that the Green Party shouldn't worry about social issues.
"That's like saying 'Stop complaining that your kitchen is on fire and focus more on your house'."
He dismissed descriptions of him as "right-wing", "a champion of capitalism" and an "enemy of socialism", just because he had a business background.
Speaking about the bailing out of banks and investors after the GFC, Mr Shaw said: "I am not a hero a free market capitalism, because free market capitalism is dead. It has been dead for seven years."
He added: "We have an economy where profits are privatised but the risks - and the social and environmental costs - of those profits are socialised."
In a reference to National, he said it was neither compassionate nor conservative to destroy rivers and streams and to subsidise businesses to damage ecosystems.
Mr Shaw, who is a new face to many, also touched on his background.
He was raised by his unionist-feminist mother in the Aro Valley until he was 12 years old, "so it was inevitable that I would join the Green Party".
Mr Shaw was elected in a delegate vote yesterday, winning 54 per cent of the first preference votes compared to Kevin Hague's 44 per cent.
Gareth Hughes and Vernon Tava each won 1 per cent of the first preference votes.
