Spurs blew a 2-0 lead to lose 4-3 on the night, with Cole Palmer scoring twice from the spot.
Postecoglou later said: "Their penalties were poor from our behalf. We didn't need to make those challenges and it was hard for us to claw it back.
"I think sometimes when you are in this position we are, you are desperate to do the right thing. You probably need a calmer approach. The guys are desperate to do the right thing and unfortunately it cost us.
"It was good enough to get us ahead in the game so I am not sure why we should change our approach. It was a game of big moments. If we score at 2-2 and go 3-2 ahead then the pressure is on them and they have to open up like we did when we conceded. But like I said, disappointing that we let them get the advantage in a way that was self-inflicted."
He continued: "You have no alternative and have to keep going. There is no other path we can take and we just have to keep showing up. The bit that was disappointing was that we showed the kind of team we can be, because they are a top side and we had the better of them but then unfortunately we are dealing with major disruptions. We have to keep persevering.
"We have got to see what the health of the squad is. We are a bit thin and have some long term ones. Between now and January there are some big games."