'Who knows?': Postecoglou uncertain over future after new 'low' for Spurs
Postecoglou's side crashed to a sixth defeat from their last seven Premier League matches to increase the pressure on the under-fire Australian.
Richarlison's 33rd-minute header gave Tottenham hope of a first top-flight win since December 15.
But Jamie Vardy levelled for Leicester less than 60 seconds after half-time before Bilal El Khannouss fired the winner four minutes later.
Furious Tottenham fans called for chairman Daniel Levy to quit throughout the match, while boos greeted full-time whistle after Postecoglou was jeered for substituting Richarlison.
Tottenham are languishing in 15th place, just eight points above the relegation zone.
Postecoglou claimed his injury-hit squad -- deprived of 10 players at present -- are still behind him, but the former Celtic boss conceded he could not guarantee he would still be around when the walking wounded eventually return.
"Who knows. I reckon there is probably a fair chunk that will say 'no'," he said.
"When you are the manager of a football club, you can be very vulnerable and isolated. I don't feel that.
"I feel like this group of players, not for me, are giving everything for the club. I have a group of staff that is really committed. I focus on that."
A 3-2 win at Hoffenheim in the Europa League on Thursday lept Tottenham on track for the last 16, while they hold a 1-0 lead in the League Cup semi-final against Liverpool ahead of the second leg at Anfield in February.
'Very committed'
Postecoglou's hopes of fulfilling his boast that he always wins a trophy in his second season lie with those competitions and the FA Cup.
But, after a run of one win in 11 league games, climbing away from the relegation zone is essential if Postecoglou is to survive the storm raging around his club.
"I really believe in this group of players. Even today, what I asked of them, some of the performances were outstanding considering what they've been through," he said.
"To me that's all positive, but ultimately, the fact that we've lost another game of football, the focus is on that.
"I have felt all along that the players are still very committed to what we're doing. That's important to me because I firmly believe in it.
"This is probably as low as we've been so far this year but I still think that in these last three months we can do something really special and I think these players believe that.
"Right now it's very hard to visualise that when you think of the current circumstances we're in."
First-choice defenders Cristian Romero and Micky van de Ven returned to training this week, while Tottenham continue to chase additions in the transfer window.
"You just have to look at our absences today and they'll all be back," Postecoglou added.
"Even missing Madders (James Maddison) today, he was so good the other night.
"All these little things that are not allowing us to get any momentum, I'm sure will change and when they change, I'm really confident we can make an impact."