The concessions also contained conditions aimed at protecting the cultural interests of iwi.
But Ngāi Tai argued it should have exclusive rights to conduct guided tours.
Ngāi Tai ki Tāmaki Tribal Trust chair James Brown said the main issue was the interpretation of section four of the Conservation Act, "to give effect to the principles of the Treaty of Waitangi".
"What does 'give effect to' really mean in terms of active protection of Treaty partner rights like kaitiakitanga and manaakitanga? Those things for us are quite ancestral, we have been doing them for hundreds of years before the arrival of Europeans.
"But for the last 178 years we have been deliberately excluded from our lands."
In its appeal the iwi said commercial activity concessions should not be granted to entities unconnected to the island, and that economic opportunities should be preserved for iwi on the motu.
The motu are popular destinations for recreational, scenic and cultural purposes.
The people of Ngāi Tai have deep historical and spiritual connections with the
two motu. A voyager in the waka Tainui, Taikehu, established himself on Motutapu.
Fullers has been operating ferry services to Rangitoto since 1988.
It offers a bundled ferry and tour service to Rangitoto and an unbundled passage-only ferry service to both motu. It does not conduct tours on Motutapu.
Motutapu Island Restoration Trust has a concession to conduct small-scale tours.
In the High Court, Judge John Fogarty acknowledged an error of law had been made when granting the concessions, but it was not enough to invalidate the decision because they still gave effect to the Treaty of Waitangi. The Court of Appeal agreed.
It also held the Hauraki Gulf Marine Park Act provided for both tāngata whenua interests and those of the general public to the "social, economic recreational and cultural well-being" of those who use the Gulf.
Manaakitanga was "undoubtedly of substantial importance" but could not displace all other considerations.
Investments and resources from both companies into the island and their operations also added weight to the decision.
In its appeal Ngāi Tai relied on a 1992 decision known as the "Whales Case", involving South Island iwi Ngāi Tahu, which claimed exclusive rights over whale watching enterprises off the Kaikōura coast.
The Court of Appeal said Ngāi Tai made too much of this case, as while Ngāi Tahu prevailed, its claim to a veto was rejected.
However, Brown said it was time for the Supreme Court to take another look at the issue.
In June the iwi had the third and final reading of its Treaty settlement legislation.
Brown said this case was of national interest in the post-settlement landscape.
"DoC is treating these other stakeholders as if they are the Treaty partners, and we are a spectator in the grandstand. This is important in the post-settlement landscape.
"An intolerable culture has manifest over decades and decades of self-assuming authority from DoC, and it requires the courts to scrutinise.
"We have guaranteed public access, people are free to walk around the island, but that does not mean commercial operators can come onto our private property. We are the authority to it, not DoC."
The iwi had requested the five-year exclusive rights to get its operations in order, before others were able to make applications.
"It does not mean we will not work with other operators, we just do not want to be the last cab off the ranks."
Minister of Conservation Eugenie Sage declined to comment.
