The 2-0 loss left Postecoglou winless in his first seven games in charge at Forest.
Post-match, Postecoglou was asked by one reporter if his job was in doubt after his poor start.
"Seriously, what’s wrong with something being hard? What’s wrong with that? Why do we want everything delivered nicely packaged?" Postecoglou replied.
"I’m sure your parents had a struggle in their life and they didn’t give up. You might even have been a lost cause at some point, but they didn’t give up on you.
"It seems these days as soon as something goes wrong, it’s right, that’s it, it’s wrong, we’ll change it. Everything that needs something fixed is invariably going to go through a tough time.
"I see it being an exciting opportunity. That’s why I took the role. I still believe that now, more so than ever before. At the same time, you’ve got to embrace there’s going to be a fight and a struggle for it.
"I’m here in the Premier League at the age of 60, you reckon I lack self-belief or don’t like a fight? I didn’t get here because of my connections.
"In fact, I’ve picked fights. I have. In the schoolyard, I’ve picked fights with people I knew would beat me up. That’s the kind of person I am.
"I totally understand it’s part of the fanfare around the Premier League that there needs to be a manager under the spotlight. It’s my turn at the moment. But like most managers, we enjoy having a challenge on our hands."
Asked if he will be speaking with club owner Evangelos Marinakis, Postecoglou continued: "I expect to have a discussion with the owner and everyone else at the club about what we’ve embarked on here, where we’re at and what we need to do, for sure. If people want to make an assessment of me after three-and-a-half weeks and seven games, there’s nothing I can do about that.
"At the same time, there’s nothing wrong with things being tough. That’s OK.
"I did have an option. I could have been sitting on the couch watching the game today and not being in the middle of it. I’d rather be here; much rather be here.
"I love a fight. So it’s a fight, it’s a struggle? So what? That’s OK.
"If people outside, or even internally, don’t think I’m the right person, it makes no difference to me. I took this role on knowing it would be a massive challenge with what we are trying to do in terms of changing the direction of the club. Nothing I have seen has changed my view on that.
"I love the challenge of taking this club to where it needs to be. I’m very confident we’ll get there."