A Labor politician has slammed Prime Minister Scott Morrison for failing to attend the historic celebration at Uluru to mark the closure of the climb.

Labor senator Pat Dodson blasted Morrison for his absence, telling The Guardian Australia it was “more than an insult” to First Nations people.

Neither Mr Morrison nor his Minister for Indigenous Australians Minister Ken Wyatt were present at the Sunday night celebration. Instead, the Prime Minister attended the Constellation Cup basketball decider between Australia and New Zealand at RAC Arena in Perth, where he sported a personalised Diamonds polo with “ScoMo” on the back. Prior to the game, the Prime Minister visited crew on the HMAS Sheean submarine.

Senator Dodson said the PM has “no appetite for entrenching a voice in the constitution” and that the absence was “a blow to First Nations people” and “more than an insult” to indigenous people.

“The Prime Minister of Australia should be here at Uluru to witness the ceremony and to celebrate with people the significance of the event and compliment the Anangu people on their generosity in sharing this place,” Mr Dodson told The Guardian Australia.

“[Uluru] is not some little plaything. This is a serious part of customary practice and culture for Aboriginal people.

“By the leader of our nation not being here to respect our culture and to finally respect the wishes of those old people who did not want anyone climbing the rock and complimenting them on what they have done to accommodate them is more than an insult. It’s an indication of the shallowness of the prime minister.”

Holding a press conference in Sydney on Monday, Mr Morrison said his schedule did not permit him be at the ceremony, however, he says it is good that the wishes of the indigenous elders have been respected and it is timely that that climb has been closed.

“Neither (opposition leader) Anthony Albanese or I were present at that event,” Mr Morrison said.

“My schedule didn’t permit me to be there. I can’t be in two places at once. I was in WA on the weekend and I was travelling back with my family from the West Australian telethon.”

The federal representative of Mr Morrison’s government at the event was Environment Minister Sussan Ley.

Senator Dodson said Mr Morrison’s failure to attend the event was a missed opportunity to highlight the importance of the climbing ban for indigenous Australians.

“He’s ducked us, the Prime Minister, and that’s a real insult to people who hold and carry customary law,” Senator Dodson told the ABC on Monday.

Senator Dodson was one of four Labor representatives who attended, including two other indigenous members, Linda Burney and Malarndirri McCarthy. Labor leader Anthony Albanese did not attend.

Indigenous Affairs Minister Ken Wyatt also failed to make the trip to Uluru, with a spokesman saying he had commitments in his Hasluck electorate in Western Australia.

“The minister supports the wishes of the Traditional Owners and welcomes the closure of the Uluru climb and has said that he ‘thinks it’s a significant point in the history of this country in terms of the traditional owners of Uluru having their say and having their wishes respected — it is a sacred site’,” the statement read.

Two days after the climb’s closure, which included a sometimes bitter debate marked by the booing of the last climbers on the rock, an inclusive party open to all was held as the sun went down over Uluru on Sunday evening.

The ceremony was attended by Goanna frontman Shane Howard and Midnight Oil singer Peter Garrett, who said the closure marks a time for indigenous people to have a voice to parliament.

Mr Garrett, a political activist and former Labor federal minister, received cheers performing hits about indigenous people such as Beds are Burning and The Dead Heart, backed by Aboriginal choir singers.

“This is a terrific opportunity and I feel like a weight has been lifted off the nation now we’ve got people off the rock,” he told reporters.

“Traditional owners have never wanted it, now they’ve had their wishes respected at last.

“It’s time for a new relationship with Aboriginal and Islander people, honouring the Uluru Statement from the Heart. Both Prime Minister (Scott) Morrison and the opposition leader (Anthony Albanese) need to get together and look closely at this document.

“That is so that Aboriginal and Islander people can take their rightful place in a nation which was theirs and still is.”

Anangu traditional owner elders who were part of the fight for the hand back of the rock to them on October 26, 1985, were delighted at the event.

Uluru is a sacred site and of great spiritual significance to the Anangu, and related to their creation myths, cultural beliefs and laws known as Tjukurpa. But the Anangu still mostly live in poverty and “while this is a time for celebration, we now have some hard work”, activist Vincent Forrester, 68, said.

He recalls helping his uncle as a child bring 44 gallon drums of water to tourists at Uluru, saying Anangu “always wanted to be involved in the tourism industry”.

Anangu were excited when the hand back occurred 34 years ago, with hopes of gaining jobs and riches from the tourism boom at the luxury Yulara resort town. But fewer than 30 are believed to work there and leaders such as Central Land Council chairman Sammy Wilson say it is time operators “woke up” and employed Anangu.

“The next chapter will be local Aboriginal park (Uluru Kata Tjuta National Park) managers for Parks Australia,” said Leroy Lester, the son of land rights campaigner Yami Lester.

“Then the next step will be providing visitors with more activities, private enterprise starting more activities now that the climb is finished, but there are other things we can do.”

with AAP