He said Goff had benefited from the support of both Labour and National's "party machines".
"We were up against a big mountain."
Goff scored 155,957 of the votes - which he said was 48 per cent of the total - compared with Tamihere's 70,822, a difference of 85,135. Craig Lord got 25,430 votes.
In an earlier statement on his Facebook page, Tamihere said: "We may not always agree on how, but we do agree Auckland can be a great place, New Zealand's leading city.
He thanked his campaign team and supporters "from the bottom of my heart".
Tamihere said their votes had sent a message that a growing number of ratepayers were not happy with many issues facing the city and that they wanted new ideas from their councillors.
"I sincerely hope they listen," he said.
Tamihere said he would return to his work as CEO of the Waipareira Trust, where he was "even more determined to transform the lives of many in need".
He is expected to address his supporters at an event in Te Atatu around 4pm.
Goff's own private polling had him comfortably ahead weeks out from the end of a gruelling campaign, which saw Tamihere pit his bravado against the political experience and workmanlike manner of his rival.
Phil Goff at the Kingslander today. Photo / Annabel Reid
Goff, 66, entered politics in 1981 as a Labour MP and rose to be Leader of the Opposition. He won the Auckland Mayoralty in 2016 with a thumping victory over Vic Crone.
Tamihere, a former Labour MP, ran an energetic campaign and rolled out a number of bold policies to "shake up" council.
They include plans for a double-decker harbour bridge, privatising 49 per cent of Watercare, selling the business of Ports of Auckland but keeping the land, and setting up an 0800 Jacinda hotline to rid the city of homelessness.
He has promised to freeze rates for three years and expects a "more equal partnership" with Wellington by way of extra taxpayer money for housing and transport.
Tamihere's unpredictable side was also on show with promises to sack the board of Auckland Transport, a complaint to the Serious Fraud Office about the sale of a council building and uttering the Nazi salute "sieg heil" in a debate with Goff.
The Croatian Club in Te Atatu, where Tamihere's election day party is. Photo / Isaac Davison
Tau Henare, a former cabinet minister and a member of the council's Independent Māori Statutory Board, has called Tamihere a "flawed genius" who lacks diplomatic skills and will "let loose the dogs of war".
Tamihere's running mate, Albert-Eden-Puketapapa ward councillor and former National MP Chris Fletcher said Tamihere could be feisty but would be an excellent negotiator and get things through.
Before the votes were released, Tamihere had said: "All of my whanau and all my support base will be heading down to the Croatian Club in west Auckland. That's where the bedrock of my support is.
John Tamihere chose Chris Fletcher for his running mate and deputy. Photo / Michael Craig
"We'll be having a big knees up down there on the shore. We're westies so it won't be orange juice."
Goff said he may have a beer at the Kingslander but wouldn't make it a late night.
He thanked his supporters for giving him the back up. The election result is the result of a team, he said.
He thanked his family, saying he doesn't know how to thank his wife who has put up with his life in politics for 35 years.
"I think we would have got strong support from across Auckland and the strong diversity of the city.
"I'm proud of the foundations we have laid. My priorities are to continue to build infrastructure, tackling climate change and the structure of council with a review of council-controlled organisation."
