In the wash-up of the Batman byelection, Richard Di Natale is looking inwards.

Not just at what went wrong in a campaign that appeared to be the Greens’ to lose but what went wrong in the party, which allowed internal fractures and divides to dominate the party’s chance to add a federal MP to its lineup.

“This was always going to be close,” he said before his only scheduled media event, a late-night appearance on the ABC, on Sunday. “We made incredible inroads in Labor’s heartland with a positive campaign on Adani, refugees and inequality, but it is absolutely clear that we have to get our own house in order if we’re going to win back traditional Greens voters who were turned off by the leaking and sabotage from a few individuals with a destructive agenda.”

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The wheels fell off the Greens’ campaign in the final weeks before the 17 March poll, with infighting, increasing factional divides and disagreements over policy directions overshadowing Alex Bhathal’s attempts to finally wrestle the seat from Labor.

Labor’s decision to run nurse and former ACTU president Ged Kearney in the seat, where Labor had seen dips in support under former MP David Feeney, was seen as an endorsement of Bill Shorten’s policies.

Speaking at Kearney’s victory party on Saturday night, the Labor leader said the party would take the “lessons and message” from the Batman byelection to Canberra, and signalled Labor would continue campaigning on the issue of inequality before the next federal election.

On Sunday, he doubled down on that message.

“It is not about us,” he said of the win. “Political parties do best when we focus on the needs of everyday people. We have a very different agenda to that of ... my opponent, Mr Turnbull. We want to see that tax breaks are working to relieve middle-class Australians.

“It is a lesson for all political parties. When you focus on the people rather than yourselves, that is what people want to see. They don’t expect us to win every argument, they don’t expect us to accomplish everything. They do expect us to spend every day trying to serve the people.”

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Meanwhile, Malcolm Turnbull, who heralded the Coalition’s retention of both New England and Bennelong as an endorsement of his government, claimed Labor could take no such comfort from holding on to Batman.

“We weren’t involved in that election,” he said. “I guess it tells you a lot about Bill Shorten’s situation that he’s crowing about holding a seat that the Labor party have had for 50 years.”

The foreign affairs minister, Julie Bishop, told the ABC: “I think the infighting amongst the Greens enabled Labor to get over the line. Otherwise it would have been a much worse result, without doubt.

“This was Labor heartland, this was one of their safest seats, 75% two-party preferred. Now it is a truly marginal seat for Labor, so I wouldn’t be taking great credit if I were Bill Shorten with this outcome.”

In the final week of the campaign, government MPs had claimed the byelection would be a comment on Labor’s $59bn dividend imputation plan, with the assistant treasurer, Michael Sukkar, tweeting on the day of the election that a loss would mean the policy would have to be dumped.

Michael Sukkar (@MichaelSukkarMP) It’s clear that if Labor loses Batman, Shorten will have to dump his rotten retirees tax. #auspol https://t.co/uOfO2GnLR9

The treasurer, Scott Morrison, told Sky News on Sunday morning that the Melbourne electorate, which is considered the nation’s most progressive, was not indicative of mainstream Australia, and Shorten’s policy still had tests to pass.

“He is pillaging your pocket to pursue his political interests,” he said. “That is not a good sign for the Australian people under a Shorten government, if they are ever allowed to [win] power.”