Abrahams, who famously goes by the nickname Moose, was speaking to the Aussie where he seemed to touch a nerve when asking him about the club's wait for silverware.
Tottenham were eliminated from the Carabao Cup back in August when they were defeated by Fulham in the second round.
And their FA Cup journey also came to an abrupt end following last Friday's 1-0 defeat to Manchester City in the fourth round.
With no European football this term and Spurs in fifth spot and currently eight points behind Premier League leaders Liverpool, it feels highly likely that the club's 16-year wait for a trophy is set to continue.
But that didn't stop Postecoglou having a little bit of fun with poor old Moose.
READ MORE ON TOTTENHAM
Postecoglou gives Tottenham transfer prediction ahead of deadline day
Simon Jordan names the manager Liverpool should consider to replace Jurgen Klopp
Speaking in Tuesday's press conference, talkSPORT's Abraham asked: "In your career it's rare that you go a year without winning a trophy, which will probably happen this year, so is top four now a success?"
To which Postecoglou replied: "So we can't win the league?"
With Abrahams insisting that's now that he meant, Postecoglou chuckled: "Well, you did. Probably? That's fine, that's OK, you're allowed to say that.
"It's fine, don't worry about it - you're allowed to say it, don't worry.
Most read in Football
Mancini storms off in disgust DURING shootout as Son helps KO Saudi Arabia in Asian Cup
Premier League 'gets VAR green light' that will change the landscape of refereeing
Everton learn when they will hear outcome of appeal against ten-point deduction
Nottingham Forest 1-2 Arsenal LIVE REACTION: Gunners close gap to Liverpool in title race
"You don't think we're going to win the league, that's fine - just be strong on that, that's alright!"
Though Postecoglou did go on to answer the question, saying: "Look, I understand that and I get the question.
Ange Postecoglou gives his Tottenham transfer prediction ahead of Deadline Day
"It's disappointing that we're out of both cup competitions, particularly with not being in Europe because our supporters are really kind of crying out for some sort of success for them to experience, but I can't let that guide my course.
"This year is still about us growing as a team, finishing the second half of the year stronger than we did in the first.
"If we do that, we'll be in a good position to continue to challenge and push this team along. That's our focus.
"As much as there's disappointment there, obviously we're out of another cup, there's also a real reminder to us that it's not just about winning one trophy.
"If we're going to compete at the level we want to, then we've got a lot of work to do."