Spurs clinched a Europa League semi-final spot with a superb 1-0 win at Eintracht Frankfurt, with the timely performance ensuring Postecoglou's fight to keep his job rumbles on.
The former Socceroos mentor admitted on Wednesday he had "no idea" if he would still be at the club after this tie.
Spurs, languishing in 15th in the Premier League, were back in the Europa last-chance saloon and up against it at Deutsche Bank Park after a 1-1 draw in the first leg last Thursday.
But Dominic Solanke's spot-kick two minutes before halftime settled the tie as Spurs showed plenty of fighting spirit to earn their first Europa semi sport since 1984.
Postecoglou can now focus on a two-legged semi-final with Bodo/Glimt in May as his side hunt their first trophy in 17 years.
"I am the same manager today that I was yesterday so if people think us winning tonight makes me a better manager or whoever thinks I wasn't doing a good job yesterday, (they) should be feeling the same way," Postecoglou said.
"I don't care, it doesn't bother me, it doesn't affect what I do.
"For me, it's always about the dressing room. Do the players believe? Do the staff believe? That's much more important than what others may make of me.
"So, unfortunately for a lot of you, you're going to have to put up with me for a little bit longer, mate, so let's see how that goes."
Postecoglou was effusive in his praise for a Spurs team who had lost James Maddison before halftime after he took a painful blow in the 38th minute from Frankfurt goalkeeper Kaua Santos to win a decisive penalty.
Amid whistles from Frankfurt's noisy standing section, Solanke rolled his penalty past Kaua before Romero, Mathys Tel and Rodrigo Bentancur went close to sealing Tottenham's passage into the last four.
With no second goal forthcoming, Spurs had to withstand a barrage of late Frankfurt pressure, but goalkeeper Guglielmo Vicario remained untroubled before the full-time whistle was met with big celebrations on the touchline and from the 2,800 away fans.
"Super proud of the lads. Going away from home, a quarter-final against a very good side, you know you're going to have to work really hard, be really disciplined," Postecoglou said.
"But it's not about my belief in the team.
"What's more important is the belief the team has had because after a season like ours, it would be very easy for the players and staff, they could have left me in a pretty vulnerable place in terms of them splintering, but I've never felt that (even) with all the noise around our season.
"They've been so united in believing in what we're trying to achieve here and that is what gave me heart all along.
"Not at any stage have I felt they lost any belief in me or what we're doing. That is crucial when you're having a difficult season."
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