Brennan Johnson struck twice for the visitors before Omari Hutchinson pulled a goal back ahead of halftime. However, Spurs took control in the second-half thanks to goals from Djed Spence and Dejan Kulusevski.
Postecoglou 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 really well in the opening 10-15 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, in terms of the second ball and duels. Disappointing goal we conceded but aside from that I thought we handled that side of the game really well, which we had to.
"But I always felt we were a threat when we had the ball. Sonny (Heung-min Son) was unplayable in the first half. So good to get Brennan back in those areas where he's always a threat. All four of our goals were quality goals. We had to do the hard things but the fruits of that labour was that our front third play was super, exciting and clinical."
On their injury-list now clearing, he also stated: "Look, we've certainly benefited from having a couple of midweeks off for sure. That's coincided with getting a few players back. You saw today we were able to rest a couple of players in Pedro and Madders. I can make substitutions and the players coming on can make a difference.
"We're certainly in a good space of using these two weeks as well as we could to reenergise the team and I think it is. We've still got some significant players out. We've got Solanke, Richarlison, Romero, Van de Ven, Ben Davies, he's out today. They're all still to come back. I just feel like we've got a really good opportunity in these next 10 days to be well equipped for what's ahead. What's ahead is obviously Europe but also an opportunity to address our league position which is obviously not good enough."