The Australian lasted just 39 days with the Premier League side, marking the shortest spell in EPL history.
He suffered six losses and two draws, with his final match being a defeat against Chelsea.
Owner Evangelos Marinakis exited his seat before the final whistle, and Postecoglou was dismissed 18 minutes after the match concluded.
The Australian was aware that the media had already caught wind of his dismissal, which made things uneasy for him behind the scenes.
He was yet to converse about his sacking with his support staff.
Wanting to escape the situation, he attempted to bypass his press obligations but heavy traffic made his getaway impossible, resulting in another awkward predicament.
In conversation with SEN 116, Postecoglou said: "I haven't told the story but it was brutal mate.
"I literally got sacked straight after the game.
"And you know what it's like after games.
"I'm in the coaches' room.
"I knew it was coming so it was one of those where I thought, 'Well, it could come any day now.'
"But they literally sacked me straight after the game and then I hadn't done the press yet, but the press already know.
"I'm walking out into the corridor, I just wanted to leave because I was going to do something I'd regret.
"And then I hadn't apokwn to the assistant coaches, who I knew also were probably going to be sacked, so I needed to say something to them.
"But I'm doing this while walking through throes of press and people who were just all looking at me.
"And I just wanted to get out of there.
"So the security, who's a really good guy, said to me, 'Ange, I know you want to get out of here, but it's an EPL game so all the roads are blocked, you won't get your car out for half an hour.'
"So I sat in my car for half an hour just by myself.
"I spoke to Georgia for a bit.
"And after half an hour, he kind of said, 'Look, Ange, the roads have opened but there's a lot of traffic down there.'
"So they did their best to try and get me through."
In a truly testing end to his stint, the traffic lights became a platform for fans from both Chelsea and Forest to launch verbal jibes his way.
Postecoglou recalls being jeered while stuck at the lights for at least 15 minutes.
He said: "But I got stuck at one set of traffic lights for at least 15 minutes.
"And I had Chelsea supporters giving it to me, Forest supporters weren't much kinder.
"I'm sitting in the car, head back, right?
"And in between, I've got little kids coming up for a selfie.
"So what do you do? I don't want to disappoint. So I paid for my penance.
"So whatever mistake I made, I paid a pretty heavy price for it."