"I had a bit of an argument with them on NXT."
The NZX launched the NXT market in 2015 targeting high-growth companies. So far it has attracted four listings.
Falkenstein said he felt the culture of the business had become too bureaucratic and more about being "traffic cops" than encouraging new listings.
Falkenstein's concerns come on the back of a report by Chapman Tripp which warned listing numbers were shrinking.
Roger Wallis, a partner with the law firm, said only three initial public offers were expected this year - a number which meant the local bourse was not sustainable.
"It is not terminal but it could be if we are not careful," Wallis told the Herald last week.
But Mark Peterson, NZX's interim chief executive, said it was important to look at the longer term trends rather than a short timeframe.
The market capitalisation of the NZX had grown from $46 billion in 2003 to $117b.
While the value of equity transactions had increased from $22b in 2010 to over $42b.
The NZX was averaging around five new listings per year, Peterson said.
"Yes we have had a couple of bumper years and some lean ones," he said.
"We would love more product. But I don't think we would call the situation in crisis or dire."
The NZX was heading in the right direction and there needed to be recognition that the market went in cycles, he said.
Peterson said the NZX was aware of Falkenstein's concerns about the NXT but the market was designed to be a long-term play.
The NZX was about to begin an extensive review of its listing rules and it will look at NXT as part of that process, which is expected to take between 12 and 18 months, he said.
"We want to grow the listed community - more than just debt and equity - and we are not really set up for that."
On being accused of being "traffic cops" Peterson said the NZX had a role to preserve market integrity.
Regulation and supervision were just as critical as seeing market growth, Peterson said.
NZX chairman James Miller said he was aware of Falkenstein's interest in standing for the board.
"This will be addressed in due course as part of our director nomination process."
The NZX has yet to name a date for its annual general meeting, when shareholders will get the chance to vote on who can sit on the board.
The company currently has a six-member - all non-executive board.
Election of a director has to have the backing of the majority of shareholders.