Tottenham are sitting down in 14th, with just 34 points from their 29 Premier League games and have also been knocked out of both domestic cup competitions.
Postecoglou told Optus Sport: “I've always said I hate telling people how they should feel. There's no doubt that a large portion of Tottenham fans have lost belief in what we're doing.
“I think they were encouraged by what they saw last year for sure, and that hasn't manifested itself.
“I'm still optimistic and bullish about the squad we've got. There's enormous growth in them once we can navigate through this and being through a tough time...surviving tough times can be such a strong uniter of people.
“Because you think there's nothing down the track which will be anywhere near as bad as what we've gone through. We've survived and we've stuck together.
“Part of that is people will see aside from the obvious - the disappointing results - they still see a squad there which I think is exciting.
“I guess the biggest way we can influence that is by giving them hope. Still got things to play for in Europe and we've got to try and finish the season off in a positive way.”