Villa boss Emery, one of the senior managers in the top-flight, will turn 53 on Sunday but he's a junior compared to Postecoglou, who, at 59, is the Premier League's oldest boss.
"Miserable day for him, I hope!" smiled Postecoglou when the subject of Emery's birthday cropped up at a pre-match news conference.
"I'm the oldest in the comp mate, so I'm not going to mention birthdays."
Postecoglou reckons visitors Villa deserve to be in the Champions League instead of Tottenham this season, but he hopes to "get on top of them" this time around.
Spurs and Villa were top-four rivals during the 2023-24 campaign and the Midlands club claimed fourth spot by a two-point margin.
Fifth could have secured Champions League football if English clubs had performed strongly across Europe's three competitions, but Manchester City, Arsenal, Liverpool, West Ham and Brighton failed to go beyond the quarter-final stage and Villa exited the Conference League in the last four.
It means Tottenham had to be content with Europa League football while Villa have hosted and defeated Bayern Munich in the Champions League.
But Postecoglou shut down suggestions that it must hurt to see Villa face Europe's elite as he's focused on cutting the current five-point deficit to Unai Emery's men.
"If English teams had only done better in Europe last year. Jeez, woe is me," Postecoglou said with a smile.
"Nah, I think they got what they deserved. We got what we deserved. We're playing where we're playing. They're playing where they're playing. We'll just try and get on top of them this year.
"We know it's going to be a good game. We'll ask certain questions of each other.
"It's a great challenge, but it's at home. We want to continue to be strong at home and need to make sure our league form is more consistent."
Spurs beat Manchester City 2-1 in a pulsating League Cup tie on Wednesday to progress into the last-eight in front of a near sell-out crowd of 60,797.
It demonstrated the appetite Tottenham supporters have for the cups given the club's 16-year trophy drought and an electric atmosphere was created to help earn a sixth home win in all competitions this season.
While Spurs have lost their last two away matches, Postecoglou is pleased with how strong they have been on home turf.
He added: "It's been strong and it has to be. The supporters play a big part in that.
"I thought they were brilliant on Wednesday night and that's part of it because if they can generate that energy in the stadium, the players certainly feed off it and it makes oppositions uncomfortable."
