Sopoaga also revealed Tonga's Prime Minister Samiuela Pohiva cried during 12 hours of talks.
Mr Morrison responded: "I'm accountable to the Australian people, that's who I'm accountable for".
The delegation is seeking to enhance ties with other nations in the Pacific region through multilateral programs at the forum, which is now in its 27th year, the ministry said.
Meanwhile, the leaders also agreed in a communique on Friday that strong political leadership to advance climate change action, protecting their ocean's healthy and integrity, sustainably managing their island and ocean resources, connecting their oceanic continent and ensuring healthy people as cornerstone priorities informed by science.
The summit's host, Prime Minister Enele Sopoaga of Tuvalu, has already stated that the new Australian adaptation fund falls short.
"Like our Pacific Island neighbours, we will continue that global call", Ms Ardern said.
The leaders said that it is clear to overcome the climate change crisis facing the Pacific Island nations, and they must increase their global solidarity and align their actions with their common concerns.
"We came together in a nation that risks disappearing to the seas, but unfortunately, we settled for the status quo in our communique", Fiji Prime Minister Frank Bainimarama said on Twitter.
"I will always be a proud Australian who will defend those industries and we will not be de-industrialising Australia".
Mr Sopoaga said language during negotiations became "flary" but insisted he was "very happy" with the result.
"I understand the deep sensitivity to these issues, particularly where we're standing. And I showed respect towards that in my engagements".
"If you are a Pacific islander and your home is going to be washed away by rising sea levels caused by global warming then this is not a political issue, it's an existential one".
The rubbish dump used to dispose of waste north of Funafuti, Tuvalu.
Australian Prime Minister Scott Morrison can expect a hard visit. "And we had a real conversation last night".
The final communique reaffirms climate change as the single greatest threat to the livelihoods, security and wellbeing of people in the Pacific, but doesn't refer to a "climate crisis".
Speaking after the marathon leaders meeting, Mr Morrison said he wanted the SIS group to be able to express its views "freely" but that its statement was not binding on the rest of the forum.
But there was no direct mention of ending coal-fired power, while calls to limit temperature rises to 1.5C and achieve zero net carbon emissions by 2050 were couched as suggestions rather than demands.