The Whites have lost six of their last seven games, while Massimo Cellino's failed takeover has left the club in financial limbo.
"It's not an easy situation but, from the owners down, we have to be singing from the same song sheet," McDermott is quoted as saying by the Bradford Telegraph & Argus. "If everything was right at the club then I probably wouldn't be here and they would have made a decision.
"But we don't have that. The senior players are going to be really important now, the ones who are playing and the ones who aren't. You always look to them at this stage and you're only as good as the experienced players at your club.
"I feel disappointed, upset, whatever the words are, and we really need to get a result from somewhere. The reason people fail in life is because they give up. Well I won't give up on this and the players won't either."
Leeds are in action this weekend when they take on Wigan Athletic.