Spurs topped the table in November before being hard hit by injuries and they are now 11 points adrift of leaders Liverpool heading into Tuesday's match away to London rivals West Ham.
Postecoglou has repeatedly insisted squad development, rather than a top-four finish, is his priority this season.
But the Australian, who guided Celtic to the Scottish Premiership title before heading to London club Spurs, has bigger ambitions, even though it is more than 60 years since Tottenham were crowned champions of England.
Asked whether he expects Spurs to be challenging for the title next term, Postecoglou replied: "I hope so. Or why am I doing what I'm doing? That's why I came to the club.
"As somebody said to me last week, 'Just do your job Ange' and my job is to come here and try to bring success.
"And if you don't think you're going to be in the title race in 12 months' time, then I don't know why I'm here."
Postecoglou was also adamant that a top-four finish in and of itself was no guarantee of sustained progress, as evidenced by the struggles of Manchester United and Newcastle this season.
"It'd probably make my life easier if I said, 'Let's make Champions League, that's great' because everyone thinks I've done a great job," he added.
"But from my perspective, I keep saying it, I look at the teams who made the Champions League this year from last year and that wasn't the catalyst for them kicking on.
"It's not their fault - it's more demanding. But I'm not going to let this club rest on where we finish this year. Where we finish should be a foundation for us being better next year."
