A Reza Ghoochannejhad goal for Charlton Athletic on Tuesday inflicted a 1-0 defeat on the Whites, who have now lost four of their last five matches, and resulted in McDermott's future at Elland Road being questioned.
While their Championship form has been slipping, matters off the pitch have been no more positive, with Massimo Cellino's protracted takeover bid being initially blocked by the Football Association.
In an passionate post-match interview, McDermott admitted that his current situation is unlike anything he has ever come across but insisted that it is not in his nature to walk away from adversary.
"I've been in football 30-odd years and I've never experienced anything like this, I really haven't," McDermott told reporters. "Both on and off the pitch. Someone's just said to me that people are saying I should resign.
"Well actually, if people know what's gone on here and what I've had to go through, then to make that suggestion...They won't see me resigning, no way, absolutely no way. It's just a joke really when I think about that.
"If I'd have come here and everything was stable and we had money available for players and everything was going right, then I could understand the sentiment behind that. Probably I wouldn't be here. They'd have made a decision and when the new ownership comes in that decision will be made, who ever it might be. At this moment in time we haven't got that decision, so we need to get that quick."
Leeds have dropped to 15th in the table, but remain 12 points clear of relegation.