Tapuae had two tries in the bank and then prop Tevita Pasikala scored the clincher.
“I was not happy till we got that third try,” King said.
He said his forwards worked hard, with the loose forwards “tackling their hearts out”.
Nuhaka coach Rongomai Wairau said he was proud of what his team achieved this season.
Many of his players were under 20 and were still developing, he said.
He felt their level of intensity wasn’t quite where it needed to be in the final.
Nuhaka first five-eighth Kristen Munro opened the scoring in Saturday’s game, slotting a penalty goal.
However, Tapuae openside flanker Isaac Hikawai scored the first try, which was converted by first five-eighth Nikau Kaimoana, putting them ahead 7-3.
Tapuae fullback Daniel Hartley scored a try with 27 minutes left to play, extending their lead to 12-3, before Pasikala dived over for his try.
Kaimoana kicked two conversions.
Tapuae captain Jeke Fatefehi said it was good to have two finalists from the Wairoa area.
He said the forwards stood up and the backs used their speed.
They were pleased that Nuhaka were unable to score a try.
“We got a bit of a lead and then time was dwindling down,” Fatefehi said.
“A couple of bounces of the ball went our way.”
A good turnout of fans travelled from Wairoa to the game and Pasikala said whanau were important to the club.
“Rugby is lonely without supporters.”
Nuhaka captain Hickson Raroa said his team “fought with strength but Tapuae dominated on the field”.
Tapuae 19(Isaac Hikawai, Daniel Hartley, Tevita Pasikala tries; Nikau Kaimoana 2 con)
Nuhaka 3(Kristen Munro pen). HT: 7-3.