Karamoko Dembele gave the Hoops the lead midway through the first half and Albian Ajeti added a second to make it 2-0 before the break.
While Conor Washington scored a second-half goal for the Addicks with 14 minutes left to play, Celtic didn't concede again and completed what was overall a dominant win, despite the narrow scoreline.
Postecoglou said he was pleased to see his philosophy already starting to sink into the players after another confidence-boosting victory.
The Australian will take charge of his first competitive game with the Scottish giant in little more than a week against Danish club FC Midtjylland in the UEFA Champions League qualifiers, and admitted he had plenty to think about ahead of the clash.
“We still need to improve on everything," Postecoglou said after the win against Charlton, which plays its football in England's third tier.
🗣️ "First-half was good, we controlled the game. For a lot of these guys it's their first game for quite a while but they worked hard and that's the main thing." 👍🍀— Celtic Football Club (@CelticFC) July 10, 2021
Ange Postecoglou on #CELCAFC! 🎙️ pic.twitter.com/f5NdDtzFPU
'It’s still only the beginning for us so all we can do is focus on a little bit of improvement day-to-day.
"We have another game coming up against Bristol City, so we’ll build towards that and, hopefully, improve our performance a little bit from today.”
While some of his players looked rusty, Postecoglou said he was pleased to see his methods starting to take effect within the squad.
“We’re working hard in training ... which probably has an effect in terms of fatigue in the games," he said.
"The most important thing for me is they’re trying to do the things we’re talking about and as long as they do that we can progress.
“They all worked hard. For me, what’s most important is the intent shown by the whole team. We’re trying to keep the ball and be aggressive when we lose the ball. I thought we had a better shape, especially in the first half, so they’re the key things.”