The Royals were guilty of a desperately poor performance at the Stadium of Light, while the hosts pulled themselves out of the drop zone, much to the delight of Martin O'Neill
Goals from James McClean, Steven Fletcher and Stephane Sessegnon secured a convincing win for the Black Cats, leaving McDermott lamenting his side's slow start to the game.
"It was a tough evening, we were struggling a wee bit with our players out. If you give away a goal in the first half, such an early goal, it gave them a lift as well so that didn't help," McDermott told reporters.
"I thought first half, we played some decent football, made some chances at the end. We have to be more solid.
"I don't fear that [the sack], no. I've been in football for 30-odd years now.
"I know this club is in a far healthier position than it was a year ago, two years ago. I've been used to winning games over a long period of time and at the moment, we're not winning games.
"We know we're in a results business and the boys have given me everything so I can't ask much more of them."
The 51-year-old also revealed the midfielder Danny Guthrie refused to travel to Wearside, citing a poor mentality as his reasoning. A club official revealed that the former Newcastle man had texted the boss to apologise for his actions after the squad had departed for the North East.
"Danny Guthrie made a decision that his head wasn't right to travel," McDermott explained. "Everyone's got to be going in the right direction, that's really important for me so you have to put yourself up for selection every single game.
"Any player has to be part of what we're about and any player can't deviate from what we've been about over the last three years, we're very much about the group, we have to be, and pull all in the same direction. It's not a conversation for tonight but something we'll deal with in the week."
The Reading boss also claimed he would not be afraid to splash out on signings in January, with owner Anton Zingarevich ready to finance big-money moves, with the Royals currently six points from safety.
He said: "The club made a decision in the summer, we didn't invest in the summer.
"We all know January is a difficult window, we're fighting a battle here so that'll be down to the owner. We are in such a strong position financially, whatever the outcome of this season.
"We want to get out of this so we have to get out of this and if that means January, we will do what we have to do."
Sunderland boss Martin O'Neill was ecstatic to pick up a win, just the Black Cats' third of the season in the league, to lift them into 15th, a place and point behind local rivals Newcastle.
"I'm delighted to have won, naturally," he beamed. "There's a sense of relief too.
"We got off to a great start. We've been chasing games here at the Stadium of Light and been giving teams leads and trying to get back into games so it was pleasing to get the first goal tonight.
"It took a bit of anxiety out of the crowd and jsut pleasing to win. The first goal will give James a massive boost in confidence. There were signs there tonight that he's returning to form."
Steven Fletcher was passed fit on Tuesday morning, and O'Neill was thrilled to have his top scorer back in action after missing the weekend's game with Chelsea and ahead of a tough run that sees them face Manchester City, Tottenham and Liverpool in their next four games.
The Ulsterman continued: "It was a big lift. I think that Connor Wickham has done fine, but Steven declared himself fit, it gave a huge boost to me and to the dressing room too.
"We've got tough times ahead at this minute, we'll just have to try and see it through but that was a boost tonight.
"I just feel that this season will be really tough for us, I accept that. I thought that anyway at the start of the year and I didn't want people to get carried away."