The axe fell on McDermott at the Madejski Stadium in early March, with a coach who had guided the Royals to the Premier League paying the price for an inability to steer them clear of top-fight trouble.
A failure to bolster his ranks in January was also offered as one of the reasons behind his sacking by Reading owner Anton Zingarevich, but McDermott says he made every effort to make quality signings.
He told the Daily Mail: "I know the owner said I didn't buy any players in January, but we couldn't agree fees for Thomas Ince at Blackpool and Gylfi Sigurdsson at Spurs.
"We made big offers for them."
It has not taken McDermott long to bounce back into the dugout, with Leeds offering him the chance to succeed Neil Warnock and set about guiding a fallen giant back to the big time.
On that challenge, the 52-year-old added: "If I had been here a couple of games earlier you never know (about promotion this season), but I was brought in with the brief to make sure we didn't get relegated.
"All I know is that I have had the backing from the owners GFH Capital to make the changes I want at the club to get promoted.
"At Reading we had players who could hurt teams and I want the same at Leeds. This club is proper."