She then paid with a $20 note - only to be given a new $5 and some change in return.
"It's good that I got change, I suppose, but it would be better if they took the new cash," she said.
And at car park A, two attempts by customers to use the new notes failed.
Jonathan Spraggs, who had used a $20 to pay for his parking, said it would be annoying if he'd tried to pay cash and got it rejected.
"Especially if you're in a hurry. Luckily for us it wasn't any issue."
Mr Spraggs said he had also seen a person try to pay for a bus recently with a new $5 note - confusing the driver who had not seen one before.
A Wilson Parking spokeswoman said all the company's machines were being upgraded to accept the new notes.
"This process will be completed across the country by mid-November, including at car parks A and B of Auckland Hospital.
She said most machines were already compliant with the new notes, with the upgrade process having begun "several" months before the new money entered circulation.
If customers were caught short, she said they could pay by eftpos or credit card, and there was a response centre available to assist any people who had problems.
An Auckland DHB spokesperson said: "We have not received any complaints in relation to this issue and are informed it will be sorted in the next week."
The new notes were officially released on October 12, but a Reserve Bank spokeswoman said " calibration banknotes" had been released in July this year "to prepare industry for change.
"We provided a four month window, as agreed with industry, for banknote manufacturers to recalibrate their machines in readiness for the new notes," the spokeswoman said.
Barry Dow, chief executive of Glory New Zealand - a company that supplies cash handling equipment to banks and major retailers - said new software needed to be written so that the machines would know to accept the notes.
He said installing the software could be a matter of downloading it which could take a few minutes of hours, but in some cases it needed to be manually installed for each machine, which could take longer.
He said the Reserve Bank had supplied them with notes in advance to the software could be written.
Last week the Otago Daily Times reported that some machines were reading the new notes as forgeries, causing confusion among consumers at some council car parks and at a mall with parking also managed by Wilson.
New $20, $50 and $100 notes are likely to be released in April.