Cellino is still waiting for the outcome of an appeal hearing after being disqualified by the Football League from completing a £25m takeover.
An independent QC heard both sides of the argument in London on Monday and revealed that he required more time to consider the case further.
Cellino was highly critical of McDermott and club owner Gulf Finance House Capital in his 22-minute conversation, but was unaware he was being recorded.
McDermott, speaking at a press conference ahead of Tuesday night's home game against Charlton Athletic, told Sky Sports News: "If you have a private conversation, it's private and shouldn't have gone out, full stop.
"It was private. What I have been saying since April is that we need a togetherness here and we'll get a togetherness. We need a resolution to come sooner rather than later. We need that unity.
"If he gets the club he'll have a decision to make on where we go forward."
McDermott has repeatedly stated he will not walk away from the club and would be willing to work with Cellino if his takeover was successful.