Those on the flight say they specifically asked for passengers to be better separated, including moving some people into the nearly empty business section.
Instead, they were reassured by the pilot that there was no need to worry as the Covid-19 situation was under control in New Zealand. A flight attendant offered further reassurance saying people on the flight were assumed to be fit to travel.
It was confirmed yesterday that a man on the flight, aged in his 60s, was now infected and is New Zealand's third active case in as many days.
Danielle Blackwell, a New Zealand citizen returning to Auckland from Spain, sat elbow-to-elbow with other passengers on the Melbourne to Auckland flight last Saturday.
She said passengers were so irate at the lax measures that a staff member addressed the issue on the intercom.
"I'm unsure who came over the speaker, but they said 'If you are on this flight then we assume that you are fit to travel'."
Frustrated passengers have spoken out after it was yesterday revealed a man in his 60s, who is in managed quarantine, had tested positive for the potentially deadly virus.
The country now has three active cases.
Director general of health Ashley Bloomfield said the man flew from Pakistan to Doha and Melbourne on June 11, and then to Auckland on Flight NZ124 on June 13.
A man in his 20s who was travelling with his wife said he was "extremely disappointed" with Air NZ's lack of safety measures on the flight.
"There had been a number of people complaining about the lack of safe distancing, especially as there was were vulnerable people on board," said the man who didn't want to be named.
"Economy class was completely full, yet there wasn't one passenger in business class."
He said the pilot acknowledged there had been complaints about social distancing but assured passengers the situation was under control in New Zealand and there was no need to worry.
"I was pretty shocked and disappointed."
Blackwell said fewer than half of all passengers were wearing masks.
"There was no physical distancing to board, and as we started boarding, everyone was like, 'hang on, everyone's sitting next to each other, we're supposed to be distanced.'"
She and many of the other passengers returning home from Covid hotspots including the United Kingdom, Spain and Germany, were shocked at the lax attitude of the staff.
The Air NZ protocol was a far cry from the strict measures Blackwell, who was tested before she left Spain and wore a mask, had seen aboard her other flights home.
"They gave you a new mask, hand sanitiser and gloves on each flight, and then it was like Air NZ didn't care," she said.
Blackwell opted to be tested again after the Ministry of Health contacted her, but says she was told it was voluntary.
Again she tested negative, but she said she anticipated more positive cases of the virus from that flight.
"If that person had it on the flight, then we were all at risk."
An Air NZ spokeswoman said cabin crew and pilots took the wellbeing of customers very seriously and were aware of the guidelines in place to protect everyone on board.
She said Air NZ was following the advice of the Ministry of Health and Ministry of Transport to keep customers and crew safe.
The aircraft was a 777-300. The economy class was 75 per cent full, while premium economy was at 52 per cent capacity and business class was at 20 per cent.
"On international flights operated by Air NZ crew are required to wear masks and gloves during food and drink service and face-to-face interactions with customers.
"Our jet aircraft are fitted with hospital-grade air systems that filter out viruses, and hand sanitiser is also available in airports and on aircraft for customers and staff to use as they wish."
The unnamed man said he and his wife were yet to be contacted by the Ministry of Health and despite being in managed isolation for five days had not yet been tested.
He called them yesterday saying he was on the flight and was told someone would come to see them - but as of last night the couple had not heard from anyone and staff at the hotel had no idea what was happening.
Bloomfield said yesterday they were in the process of contacting people on board NZ124.
The Ministry of Health was now advising that medical grade masks should be offered to passengers on international flights and they should be strongly encouraged to use these masks as a precautionary measure while on board.
"These masks should come with instructions for proper use, alongside crew instructions in the safety briefing," a ministry spokesperson said.
"Hand sanitiser should also be made available on the flight. For safe use, enough masks need to be available for changing as appropriate throughout the flight, and there need to be facilities for safe mask disposal."
New Zealand now has 1157 confirmed cases of Covid-19 - 1507 in total, including probable cases.