Pacific leaders have expressed disappointment after Australia voted against altering its constitution to create an Indigenous voice to Parliament over the weekend.

Had it won, the referendum would have established a representative body to advise the government on issues that affect First Nations people.

Former Pacific Island Forum secretary-general and PNG diplomat Meg Taylor said consultation in the lead-up to the vote was poorly managed.

“From watching it from afar, you never got a real sense of how the proposal was constructed. And from the last days, you had Indigenous Australians who didn’t know anything about it,” she said.

“I think the process could have been more inclusive and more thorough. I think process has a lot to do with outcome, having worked in those fields. You’ve got to really invest in the process so people aren’t confused,” Dame Taylor said.

The no vote in the referendum rejected constitutional recognition through a voice to parliament but did not reject the policies of truth telling and treaty-making, several Labor MPs have argued.

As the government seeks a way forward on reconciliation and closing the gap that respects the outcome of Saturday’s vote, Graham Perrett and Michelle Ananda-Rajah have both noted in comments to Guardian Australia that voters rejected the “specific” proposition put at the referendum.

Marion Scrymgour, the member for Lingiari – which covers all of the Northern Territory outside Darwin – also raised the prospect of continuing to push for another form of recognition to allow Indigenous communities to be heard.

Labor is considering a listening mechanism for Indigenous leaders to provide advice directly to the prime minister to help close the gap in Indigenous and non-Indigenous outcomes.

Under continued attack from the Coalition to restate Labor’s support for the remaining elements of the Uluru statement from the heart, treaty and truth telling, Anthony Albanese told reporters on Tuesday that “the expectation that the next step should be developed over days, is not respectful”.

In comments to Labor’s caucus, Albanese said the government “should be proud of the good faith we showed in responding to a request from First Nations communities” by putting the voice to a referendum.

Albanese stressed the difference between elections and referendums historically, while adding that the campaign had also reinforced the image of the opposition leader, Peter Dutton, “as someone who only says no”.

Perrett, the member for Moreton in Brisbane, said the government remained committed to closing the gap, consulting and listening to First Nations people.

“It was recognition and voice that were rejected, those were the 92 words put to the people,” he told Guardian Australia. “We don’t need to extrapolate beyond that what was the will of people when they voted.”

Asked about treaty and truth, Perrett said that “no one spoke to me” about other elements of the Uluru statement, but “there was misinformation about other things”.

Ananda-Rajah said it was premature to discuss the government’s next steps. She noted the referendum “was a specific question” and said it was “fair” to summarise the vote as no to recognition and voice, but not to treaty and truth.

“It doesn’t mean there is no appetite to close the gap – Australians want us to make progress on intractable problems,” she said.

“They said no to a particular way, so we need to find another way.”

Scrymgour, an Indigenous woman with cultural links to the Tiwi Islands and central Australia, noted the NT had a majority no vote, but that “Aboriginal communities throughout Lingiari voted overwhelmingly in favour of change”.

“The referendum was about recognition for them, a Voice for them and they told the country what they wanted,” she said in a statement.

“Given the referendum result nationally, there will be no amendment to the Australian constitution, but I will be doing everything I can to find other pathways to deliver on the votes my mob out bush have cast – so that they can achieve recognition and a way for them to be heard as First Peoples communities.”

Jerome Laxale, the member for Bennelong, said the parliament must continue on the task of improving outcomes for Indigenous Australians.

“This was an invitation from Indigenous Australians. It’s appropriate we go back to them and understand what’s next,” he said.

“We also need to understand why people said no. People didn’t vote no to hold Indigenous Australians back, they said no for a myriad of reasons.”

The Labor MP Josh Wilson told parliament on Tuesday that “irrespective of whether Australia voted yes or no, the work of reconciliation and closing the gap had to continue … It wasn’t going to be done with a yes vote and it isn’t done with a no vote.”

Other MPs said privately that the “emphatic” verdict would necessarily limit the government’s options, and that treaties will now likely need to be concluded by states, not the commonwealth.

Earlier, in question time, Albanese said he would “give respect to Indigenous Australians who have asked for a week to consider their position”, in reference to the week of silence to grieve the referendum result.

Albanese confirmed that the special minister of state was working on legislation for truth in political advertising, citing “dangerous” misinformation, including an example of antisemitic material campaigning against the voice.

Albanese criticised Dutton for “a change between yesterday and today” and “between [Channel Seven’s] Sunrise and [Channel Nine’s] Today”, in relation to mixed messages the opposition leader has sent about a second referendum for symbolic constitutional recognition.

The Liberal MP Keith Wolahan told parliament it will be a “long time before we have another [referendum] again”.

At a press conference in Canberra the deputy opposition leader, Sussan Ley, said it was “not fair enough” for the government to take time to chart a way forward. When asked about the Coalition’s own policy, Ley said: “Well, let’s see how the dust settles.”

Kate Carnell and Sean Gordon, co-conveners of the Liberals for Yes group which campaigned for the voice, said in an email to supporters on Tuesday that they “continue to hold a shared hope for the recognition of our First Peoples, greater respect for Indigenous cultures, and better solutions to close the gap”.

“We’re proud that we demonstrated how constitutional recognition and empowering Aboriginal and Torres Strait Islander communities is consistent with Liberal values,” they said.