Spurs have won only four of their last 14 fixtures in all competitions amid a horror run of player availability, which has seen them fall down the Premier League table to sit only eight points above the relegation zone.
Manchester United boss Ruben Amorim recently claimed his side were in a survival battle, but they have moved ahead of 14th-placed Tottenham.
Postecoglou is eager for his patched-up squad to get back on track on Sunday at Everton and has not lost his stomach for the battle on his hands despite being winless in five in the division.
"I understand how, externally, it may look and feel for somebody like me, but part of what I love about what I do is that there is this constant search for solutions and how to overcome challenges," the 59-year-old reflected.
"I enjoy that bit. I always reflect on the alternative, which is me not being involved. OK maybe I look a bit younger and a bit more handsome but I would be pretty bored! If I was sitting at home, I would be saying, 'I wish I was there'.
"Knowing me, I probably would be saying, 'I wish I was at Tottenham right now, I would love to see how we can get out of that situation'.
"I understand that, externally, you're probably going, 'God, he must be living a nightmare at the moment', but it's not my existence.
"It's a big challenge, I get it. I've said before that the responsibility weighs heavily on me, I feel it. I feel the pain of it. I feel the disappointment of it, but I'm a fighter and this is where I want to be.
"I want to find a way to get us out of this so we can reap the rewards of the tough battles we've had, because of that context, it doesn't affect me in the way that people may assume."
Tottenham's plight has not been helped by injuries to key figures goalkeeper Guglielmo Vicario, and defenders Cristian Romero and Micky Van De Ven, with the trio unable to complete 90 minutes since November 23.
Spurs have also been without a number of attackers, which has contributed towards Dejan Kulusevski and Dominic Solanke - arguably the club's most consistent performers this season - recently running on empty after non-stop action.
James Maddison and Tottenham captain Son Heung-min have repeatedly failed to hit top form this term, while Yves Bissouma was withdrawn at half-time of Wednesday's 2-1 loss at Arsenal where 18-year-old pair Archie Gray and Lucas Bergvall were among the club's best players.
Postecoglou hailed his teenage duo, admitted: "I agree that our young players are certainly standing up.
"Whenever you're in a situation like ours, my experience tells me you do need the ones who've maybe been through the tougher times to lead you through it. There's no doubt about it, so that's what we're looking at.
"The ones who do, whether that's Sonny or Madders, or Ben (Davies) who's back now and Dom to a certain extent, although it's his first year at the club.
"Maybe a Bissouma, we don't have a great deal of experience to lean on in these times, but, certainly, for us to get through it, it's going to need some leadership.
"Now, leadership can come in all forms and maybe it will be the young ones that do get us through, there's no reason why they can't. That's the message I've been giving back to them."
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