McDermott was informed on Friday night that he had lost his job following the takeover by Italian businessman Massimo Cellino, but then he was reinstated the next day as it was revealed that the takeover by Cellino had not been completed.
McDermott was not at Saturday's Yorkshire derby against Huddersfield Town, but his players and a 30,000 crowd at Elland Road rallied behind him to inspire a 5-1 comeback victory.
Speaking at a news conference at the club's training ground today, McDermott told reporters: "It would have been very easy for me to walk away; that was the advice I had but there was no way I was going to, all it has done is to give me more drive.
"Why would you walk away from being Leeds United manager? It makes no sense."
McDermott also admitted that he was unsure if he still had a long-term future at the club.
Leeds, who are 11th in the table, next travel to bottom club Yeovil Town on Saturday.