Forest were outclassed as the Gunners won 3-0 through goals from Martin Zubimendi (2) and Viktor Gyokeres.
Afterwards, Postecoglou said: "Obviously a disappointing outcome for us. They're a good side and at home, they're a tough proposition.
"Can't fault the lads' effort but we struggled to get a grip of the game and the second goal after half-time just allowed them to get away from us. Disappointing but can't fault the effort.
"This week, it's fair to say, was fairly disruptive for the players. International week as well so they didn't get in until Thursday or Friday then with a new manager, I'm trying to implement new things.
"So it's entirely understandable that they probably haven't got clarity of thought at the moment. But that's my job to try and embed that over the new few weeks and I'm sure we will because there is a willing group of players to do that."
On the job ahead of him, the Australian added: "It hasn't been an ideal prep for the players and you have to take that into account. All you can ask for is effort and unfortunately, against a very good opponent, today was a bridge too far.
"This is a group of players who showed last year how hard they fight for each other. Disappointment today but there's only one way to respond.
"They're all big jobs. I haven't taken over an easy one yet but that's why I'm here. I love the challenge and we'll get to where we want to."