"A few calls didn't go our way. Well a few... it felt like no calls went our way. It's hard to work from there."
Referee Rasta Rasivhenge is a member of the South African Rugby Union (SARU) Elite Panel.
Coach Gordon Tietjens said he was proud of his team's effort in defeat and said they were 'penalised off the park'.
"They put in a gutsy performance against the number one seed. We had chances there to perhaps win it. It's tough to take but it is what it is. We've got to get on with it," he told Radio Sport.
"Proud of the guys and the way they played. We defended with six for a while and then put seven points on them and stayed in the game. We got penalised off the park really.
He added: "I want to see the video before commenting on refereeing decisions that were made. The players are pretty disappointed with some of them that were made. I'll look at it and perhaps comment later on.
"You're not going to turn that result around it's Fiji's win."
New Zealand led 7-5 at halftime courtesy of a converted try to Gillies Kaka but Fiji hit back after the break through Jerry Tuwai and then were staunch in defence to deny New Zealand.
New Zealand only snuck into the quarter-finals thanks to the rugby sevens series champions when Fiji beat USA in pool play, handing the All Blacks sevens the final quarter-final spot.
The defeat was New Zealand's third of the tournament and second of the day.
Earlier the All Black Sevens, shocked by Japan on day one, only qualified on for-and-against differential by one point after a 21-19 defeat to Great Britain.
Needing Fiji to beat USA by five points or more in the final pool match to snatch the last position, the Kiwi side watched the Fijians hold on for a tense 24-19 victory over the spirited Americans.
In the other quarters, France play Japan, Argentina meet Great Britain and Australia play South Africa.
In their last pool match against Great Britain, New Zealand slipped to a 21-0 halftime deficit before roaring back after the break with three tries.
Giant-slayer Japan's earlier defeat of Kenya meant New Zealand had to win to assure themselves of a quarter-final position.