Town started very much on the front front in Suffolk, with juggernaut striker Liam Delap giving youngster Gray, playing out of position in the centre of defence, a torrid time.
But they got on top with a quickfire double from Brennan Johnson, after superstar Son Heung-Min got the better of the Town defence.
And though the Blues got a goal back through Omari Hutchinson, Spurs pulled away in the second half to record what ended up looking like a comfortable win.
Speaking after the game, Postecoglu said: “We had to work hard today, we knew we’d have to work hard. Ipswich are one of the hardest-working teams in the league.
“At home they’re fighting for every point. I thought they started the game very well, the first five minutes with the energy in the stadium.
“But I thought we did the hard things really well. A couple of times in the first half we lost a bit of concentration and some of our second ball and duels and (it was) a disappointing goal that we conceded.
“But aside from that I thought we handled that side of the game really well, which you have to, but I always felt we were a threat when we had the ball.
“Sonny (Heung-Min) was unplayable in the first half, and so good to get Brennan back, in those areas where he’s always a threat. I think all four of our goals were quality goals.
“So we had to work hard for it, but the fruits of our labour was that our front third play was super – exciting and clinical.”
Of Gray, he enthused: “We know he’s playing out of position, and Delap’s a handful for anybody in this league. That first few minutes he caused him some problems.
“But I love that Archie takes on that challenge – he doesn’t shy away from it, he doesn’t hide, he just keeps going.
“We’ll get enormous growth out of him from this period, but right now he’s contributing and helping us.
“We had to do some defensive work today, not a lot, but the defensive work we had to do was important, against a real top striker, and I thought he handled it well.”