Postecoglou took issue wiht Davison first asking him about cupping his ear towards Spurs away fans after Pape Matar Sarr had appeared to score an equaliser before it was ruled out by VAR.
"Yeah, I wanted them to be happy, mate," Postecoglou said. "We'd just scored a cracking goal. So I wanted them to cheer – because they haven't had a lot to cheer about."
Postecoglou cupped his ear again when fans barracked him for changing Sarr for Lucas Bergvall.
"It's not the first time my substitutions have been booed. If you followed my tenure, it's not the first time. They're allowed to boo. But I wanted them to cheer – because I thought it was a cracking goal."
Davison then said: "You said in the week – in your interview with Mark Schwarzer – that you felt you'd lost a portion of the fans. Is that what we saw tonight?"
Postecoglou replied: "I get it, Pat. You're trying really hard. That's fine. You've already decided what the outcome is."
Davison said: "There's no agenda."
On Sarr's goal being denied, Postecoglou then said: "It's killing the game, mate. It's not the same game it used to be. We all sat on our couches last night and watched TV – I guarantee you, if (Thursday's VAR) Jarred Gillett was the VAR last night, we'd have got a different outcome."
Postecoglou was reacting to Everton defender James Tarkowski escaping a red card for a first-half challenge on Liverpool's Alexis Mac Allister.
"You just don't know what you're going to get. We waited for six minutes for something that apparently the VAR thought was clear and obvious. It's madness, mate."
Davison pressed Postecoglou on Sarr's VAR call.
"Look, Pat, you can try and force me into a corner," replied the Australian.
Davison: "I'm not trying to force you into anything."
Postecoglou replied: "Did you think last night was clear and obvious? How many minutes did it take this referee to figure out whether it was clear and obvious? In your basic knowledge of human vocabulary – 'clear and obvious' – what does that suggest to you?"
Davison admitted: "No, it's maybe not clear and obvious. I do think it's a foul (by Sarr), if I'm honest."
Postecoglou: "OK. Right. Well, there you go. So the referee didn't see it. He then needs to see it for six minutes, but you get the right outcome so you're happy – and that's why the game's going the way it is. And I guess people like you will continue to be happy sitting on your couches waiting for six minutes for clear and obvious stuff. That's fine. I don't agree with that, but that's fine."