Spurs will face Manchester United in the final on 21 May in Bilbao, with the chance to secure their first European trophy in over 40 years.
However, Postecoglou is reportedly aware that lifting the Europa League title may still not be enough to save his job, given Tottenham's dire domestic form.
Currently sitting 17th in the Premier League, Spurs have lost 20 of their 36 matches and are on course for their worst league finish since their relegation in 1977. The dismal campaign has only reinforced the club's reputation for faltering at the final hurdle.
Tottenham's long-standing trophy drought adds further weight to the upcoming final. The club's last major silverware came in 1991 with an FA Cup triumph under Terry Venables, while their most recent trophy of any kind was the 2008 Football League Cup, a competition often regarded as minor.
"I knew throughout my tenure last year, that's what I was going to be judged on. so now we have an opportunity to do that," said Postecoglou.
"For me personally, great, it's another trophy I can reminisce in my old age about, but more importantly it's what it means for the club.
"When you look at the historical backdrop of this club, and what it's been through in the last 20-odd years, I feel it could be a turning point in terms of the way the club is perceived, but also more how it perceives itself, which I think is the biggest thing.
"That's the hurdle this club has to overcome because it'll always be there. Until you actually do it, then you are fair game for people to say 'you've always fluffed it on the big stage.'
"Irrespective of what the opposition say, or what anyone else says, what you've got to try and do is break that cycle. Whatever motivation you need to do that, you tap into."