Celtic is unbeaten in three pre-season matches since Postecoglou was unveiled as Neil Lennon's replacement in June, but the match against the Robins was the first time the Hoops have been held scoreless.
Postecoglou appreciated the sterner test of his side's credentials ahead of a run of games which includes the first leg of its UEFA Champions League qualifiers against FC Midtjylland.
“It was a tough workout for the boys,” Postecoglou told Celtic TV. “We had a really solid session yesterday, but to be fair, I thought we started well and for the first 45 – 55 minutes I thought we were really good.
'Tonight was another challenge, for sure, but the most important thing is that we want to dominate games and be the team that makes the other team adjust.'
“We dominated the game, we played in their half, we created chances and we didn’t allow much. There were some real positive signs, but it’s a fine line for us, we’re trying to get as much work into the boys as possible without compromising their wellbeing.
Of concern for the manager were injuries to Karamoko Dembele, who suffered a head knock, and Mikey Johnson, who left the field with an apparent hamstring injury, on a night the club announced the signing of Israeli rising star Liel Abada from Maccabi Haifa.
“We picked up a couple of injuries today which is disappointing but overall I think in terms of the football, it was another positive step," Postecoglou said.
“Tonight was another challenge, for sure, but the most important thing is that we want to dominate games and be the team that makes the other team adjust. For the most part, I thought we were really good at that.
“We’re not great on numbers at the moment, so it’s a bit disappointing that we may have lost a couple tonight. But we’ll see how it all washes up and hopefully it’s not too bad.
“I’m obviously excited about fans in the stadium on Saturday, but I think the whole group is. It’ll be a different experience as there will be 2,000 there – but I’m sure they’ll make a lot more noise than that.
“I think the whole playing group and all of the staff are looking forward to being back at Celtic Park and having supporters there.”