Johnson scored a second goal in the week after having closed his socia media accounts due to fans abuse.
Postecoglou said: "Brennan's had a top week. He scored in the cup to get us through, scored the winner and he scored a fantastic goal again today to get us ahead and he was a real threat all the way through.
"He had a bit of a tough period last week and sometimes it gives you perspective about what's important and what's important to Brennan is that he's a much-loved teammate and like I said last week, he works hard every day and I got no doubt he'll make a big impact for our club.
"I had my say on social media and all that sort of stuff during the week. But anyone who watches Brennan play, if they think he doesn't give everything he can every week and work as hard as he can for the team and how much he cares, I'll be very surprised.
"But that's to one side. For every footballer you've got to go through difficult moments and he's handled it really well. Like I said, I think it gives you a perspective that when the next difficult moment comes - inevitably it always comes - I'm sure he'll know what's important to him."