McDermott is back in charge at Elland Road after he was briefly relieved of his duties on Friday night by a lawyer representing prospective new owner Massimo Cellino.
Cellino's purchase of a 75 per cent stake from current owners GFH Capital is still subject to Football League approval, and GFH confirmed after the 5-1 win over Huddersfield on Saturday that McDermott remains manager.
As the chaos unfolded, McDermott consulted the League Managers' Association and spoke to several unnamed football figures but was adamant it never crossed his mind to walk away from the club.
McDermott admits he has no idea how long he will remain manager, although there was some encouragement on Sunday when Cellino told the Sunday Telegraph he is happy with the current boss.
Greeting the press at the club's Thorp Arch training ground on Monday afternoon, McDermott said: "You didn't expect to see me, did you?
"The reason I'm sitting here is, firstly, I've been reinstated, but this is Leeds United and I want to be Leeds United manager.
"I've spoken to a lot of people in the game - a lot of very important people - who said 'you shouldn't go back', but if you saw the support the team, the staff and personally I got on Saturday, it was incredible.
"I'm completely proud of the players, staff and fans - they all came together and it was a fantastic day. That's why I'm back.
"The fans are a class act - it's their football club, it doesn't belong to anyone but them. Whoever takes this club on has to have them first and foremost in their minds. Nothing else matters."
McDermott revealed the team he had prepared for Huddersfield was changed following his 'sacking' as it appeared Cellino's long-time friend Gianluca Festa was set to take over.
The original team was reinstated by assistant Nigel Gibbs once GFH had spoken to McDermott, who followed Saturday's game "watching Sky Sports" and has been assured "all football matters" are still in his control until any change of ownership goes through.
That proposed takeover by Cellino's Eleonora Sport Ltd could yet be complicated if the Football League does not sanction the deal, and Yorkshire-based consortium Together Leeds said on Friday they remain open to talks with GFH.
Another consortium, Sport Capital - headed by the club's current managing director David Haigh and businessman Andrew Flowers - saw their own takeover collapse before the Cellino deal was struck.
The uncertainty means McDermott cannot even be sure he will be manager this weekend, but he said: "No way was I ever going to walk way. Why would you walk away from being Leeds United manager?
"We need to move forward as best we can and put this to bed. The ownership needs to be resolved very, very quickly. What happens in the future I don't know."
Cellino is the owner of Italian side Cagliari, who claimed on Saturday their player Andrea Tabanelli had joined Leeds on loan.
McDermott did not name Tabanelli, but confirmed "an Italian player" had been at training on Monday accompanied by Festa.
He said: "I'm not sure deal has been ratified. I don't know the player - he came on transfer deadline day. If he has been ratified he will get the utmost respect and opportunity, if we feel he can help us."