Josh Frydenberg has played down the need for a significant shift in the Morrison government’s stance on climate change before the next federal election after the strong protest vote in the seat of Wentworth.

The treasurer and former energy and environment minister Josh Frydenberg told Sky News on Sunday people in Sydney’s eastern suburbs were concerned about climate change, but he said the government did not intend to “reduce emissions at the expense of people’s power bills”.

He said the backlash in Wentworth was driven more by the anger of local voters about Malcolm Turnbull’s removal from office two months ago than about frustration with a lack of climate action.

Frydenberg said the government had met previous emissions reduction targets and declared Australia would “beat our future targets” – despite official government figures on emissions suggesting Australia will not meet the Paris target on current projections, and the lack of a settled policy roadmap to curb pollution.

Scott Morrison backed Frydenberg’s signal in a press conference later on Sunday morning. “On climate policy, we have got that right,” the prime minister said.

While the level of community concern would vary in communities across the country, an exit poll funded by progressive thinktank the Australia Institute after people in Wentworth cast their votes on Saturday suggests climate change was a significant factor in the poor result for the Liberals.

The exit poll of 1,049 respondents indicated 78% of the sample nominated climate change as having some influence on their vote in the contest, with 47% saying it had a lot of influence on their vote, and 33% nominating climate change as the most important issue.

The poll backs Frydenberg’s primary contention that the number one issue for former Liberal voters switching to Phelps was the leadership coup against Turnbull, with 44% nominating that – but it also shows climate change was the second biggest issue on 28%, a result that would be replicated in other inner-metropolitan seats.

The activist group GetUp was active on climate change during the Wentworth battle.

“People have been knocking down our door desperate to do anything to send the out-of-touch Liberals a message that ignoring climate change is both dangerous and unforgivable,” said GetUp campaign director Miriam Lyons.

She said unless the Liberals reconsidered their current policy settings “not even its safest seat is safe”.

When conservatives moved against his leadership in late September, Turnbull attempted to appease his internal enemies by dumping the emissions reduction component of the national energy guarantee – a policy that sought to combine emissions reduction with an obligation on energy retailers to supply sufficient quantities of dispatchable power to ensure grid stability.

Morrison has formally dumped the policy since taking the prime ministership, meaning there is no emissions reduction policy for electricity mapped out to 2030, and the government also proposes to wind down the renewable energy target after 2020.

Despite mulling the options throughout this parliamentary term, the government has not been able to move forward with new emissions standards for vehicles because of internal opposition within the Coalition.

The government has signalled it might seek to boost its climate credentials by increasing funding for the near-moribund emissions reduction fund – a policy which the Coalition was transitioning away from when it worked up the Neg – but the outlook is not yet clear.