The former Celtic manager is currently in charge at Spurs as they push for a top four finish.
Postecoglou’s team started the season poorly, but are now emerging as contenders, having beaten Aston Villa 4-1 at the weekend.
Speaking to BBC 5 Live, Hart said: "My last three managers in England, David Moyes, Sean Dyche, (and) Jose Mourinho. All top, top managers in their own right and have done incredible things.
"But they are very much (about) hard work, dedication, learning what you need to do and going out and performing.
“Then I went and had three years (at Celtic) – two of them with Ange Postecoglou and one of them with Brendan Rodgers. Ange Postecoglou blew my mind because he really opened me up.
“I always thought playing out from the back, does that mean I have to do (Johan) Cruyff turns, pick passes? No, it doesn’t; it means I need to stand on the ball and make sure my centre halves are on either side of me; my six is showing.
“I’m not playing out for the sake of it. I’m playing out to score. If that full press comes and all I see is opposition players next to mine, I'm given that clarity in my mind that there's a little dink into the striker's chest.
“All these things come together, and it’s a totally different game and a totally different thought process.
“I feel truly blessed because I would honestly feel out of my depth sat here three years ago trying to have this conversation (about playing out from the back).”