Asked why fund managers voted against his re-election, he said the obvious reason is the company's depressed share price.
"Nothing personal in it, it was a protest vote."
"What I would say is that I have enormous respect for the NZME team. It's a challenging industry, and starting with [CEO] Michael Boggs, they are doing a fantastic job."
In a brief statement posted to the NZX, NZME said independent director Carol Campbell would chair today's meeting.
"The directors will discuss a new chair for the company at a board meeting next week. An announcement regarding NZME's new chair will be made after that.
"The board thanks Peter for his service and wishes him well with his future endeavours.
"The board would like to reiterate its confidence in NZME CEO Michael Boggs and his Executive Team. Michael has led the business through an incredibly challenging time, including the crisis phase of Covid-19."
Cullinane was appointed chairman of NZME in December 2017 following the retirement of the late Sir John Anderson.
A former international marketing executive and founder of high-end dairy company Lewis Road Creamery, Cullinane chaired the board through a controversial period as NZME made multiple attempts to merge with, or buy, fellow media company Stuff.
That process came to a shuddering halt last month when Stuff-owner Nine broke away from talks with NZME and sold the business to its chief executive Sinead Boucher.
Cullinane had been up for re-election at today's meeting, along with director Barbara Chapman.
NZME's notice of meeting on May 15 stated that Cullinane had the full support of the board.
Today's meeting also hears three motions from shareholders, including one seeking the company's break-up to release value, and another calling for a focus on paying dividends.
Neither proposals were supported by the Board, which also has support from the Shareholders Association on those issues.
Subscription surge
In material to be delivered at today's annual meeting, NZME said it had experienced a surge in online subscriptions in the past four months, partly offsetting an otherwise difficult trading period as the advertising market was hammered by Covid-19 restrictions.
NZME, owner of the NZ Herald, several radio stations including Newstalk ZB and online resource tools OneRoof, said its premium online subscription platform had experienced strong growth.
New Zealand Herald Premium now has 70,000 subscribers. This includes over 36,000 paid digital subscribers, up 70 per cent in just four months, and 34,000 eligible print subscribers who have activated their digital subscription as part of their print bundle package.
In February NZME reported a 4 per cent increase in full-year operating profit to $19.7m but posted a net loss of $165.2m after deciding to impair the value of intangible assets to account for a lower share price.
The company said it was impossible to predict with any accuracy the impact of the pandemic on NZME's full-year financial performance.
However, it expected first half 2020 operating Ebitda, including the wage subsidy, to be higher than that achieved in the first half of 2019.
Radio revenue market share continued to increase, year-on-year. Content changes in progress and will be completed in June 2020.
NZME's real estate arm, OneRoof, had become the largest platform for sales listings in Auckland. Its sales listings increased to 81 per cent of NZ residential listings.
The impact of Covid-19 had been significant with advertising revenue in April around 47 per cent lower than April 2019 and May 39 per cent lower than May 2019.
For June, NZME expected revenue to be around 30 per cent lower than June 2019.
Last week NZME said it had negotiated terms to extend its existing debt facilities by 18 months.
The new $110m facilities will step down each year to a level of $75m at December 31, 2022.
In 2019 NZME's net debt reduced by $23.6m to $74.7m.
NZME's shares last traded at 32.5c, down one cent. The stock has dropped by 34 per cent over the last 12 months.