But the Australian insisted he would not temper the workload demands he puts on his players.
Postecoglou made 11 changes for the visit of Real Betis and there were plenty of positives in a 3-2 win including Ewan Henderson's first Celtic goal and promising debuts for former Sheffield Wednesday pair Osaze Urhoghide and Liam Shaw.
But the main story of the night was the double injury blow which could leave Celtic without a recognised striker for Sunday's visit of Motherwell as Giorgos Giakmoumakis is recovering from minor knee surgery.
Postecoglou said of the injuries: “Albian’s one looked fairly significant. Kyogo, we are not really sure. So we will just wait and see when they are assessed.”
Furuhashi has already had a muscle injury lay-off this season along with the likes of Carl Starfelt and Tom Rogic, while Jota and James Forrest were both unavailable through injury against Betis.
Postecoglou believes a heavy schedule is taking its toll - David Turnbull had started all 30 of Celtic's previous games this season before coming off the bench to score a penalty winner against the Spaniards.
"And I guess it's the way and the manner in which we play our football as well, it's very demanding on the players. We don't have the squad yet to cope with that and that's putting stress on, which we have had to deal with pretty much the whole way through.
"We still have seven games to go, remarkably, between now and the break. Hopefully getting some game time for guys means they become options for us in terms of making them game-ready.
"Hopefully when the break comes we will get reinforcements and come out stronger."
Postecoglou, who could be facing a striker shortage for the Premier Sports Cup final against Hibernian next week, added: "I do think it's too many games.
"If we had a little more depth in our squad, then potentially it wouldn't be as much of an issue as it is right now. But there's no doubt, if you want to maintain high-quality football and have players playing at their optimum levels, it's too much to ask players to play every three days.
"But ultimately we want to be in the cup final and we want to be in Europe, so we just have to learn to cope."
The Celtic boss will not tone down his requirements.
"It's not possible," the former Australia head coach said. "It's just a by-product of the team we want to be. It's part of the process. It's nothing new to me. I have been through this process a number of times with teams I have taken over and the initial stages are always challenging for everyone.
"You try and mitigate the risk as much as you can but games are coming thick and fast and we don't have the depth we need right now and are putting players under undue stress.
"But that's the levels we want to be at. I would rather try and maintain those levels than compromise and potentially slip in terms of the football we are playing, and that affects our performance."