Celtic cruised through with a 3-0 win over Raith Rovers thanks to goals from Jota, Liel Abada and David Turnbull but Postecoglou revealed afterwards that he had lost two more attacking players.
New striker Giorgos Giakoumakis was set to make his debut off the bench but suffered a calf injury during the warm-up which caused enough concern for him to be sent for tests.
Winger Mikey Johnston was also missing after picking up a minor injury in training days after returning from a hamstring problem to make his first appearance of the season at Livingston.
On Giakoumakis, who arrived from VVV-Venlo on deadline day, Postecoglou said: "We have sent him off for a scan. There's something looming over me at the moment just to challenge me every day and we will just have to cope.
"It has been challenging but we just have to work through it and build resilience. We went through the first period of the season really short at the back and now I think I had four full-backs and three centre-backs out there.
"Now we have some great players in the front line but we can't get them on the field."
Postecoglou was already missing Kyogo Furuhashi, James Forrest and Karamoko Dembele and his bench was full of defenders and defensive midfielders.
"We did what we had to do," he said about the game. "We knew we would have the majority of the game and we had to stay patient. We got the first goal and were pretty comfortable after that and I'm pleased we got to the semi-final.
"It's going to be a tough game, you are not going to get an easy game in the semi-finals. They are a good side, they did well in the cups last year and are doing well this season and also did really well in Europe.
"The key thing for us is we are in there with an opportunity now and playing at Hampden will be special."
Raith boss John McGlynn felt his players acquitted themselves well as his side held out for the final half hour despite getting Dario Zanatta sent off for two bookable offences.
"Our guys put a lot into it and were hard to break down," McGlynn said. "But you switch off and it costs you goals, the higher level you play.
"To be fair with 10 men we did very well, kept our discipline and shape and worked hard.
"Overall the Premier Sports Cup has been very good for us, we did really well to get out the group stages, beat Aberdeen and enjoyed coming here. I'm very proud of what the players put on."