The 23-year-old was a summer arrival in 2023, coming into the club around the same time as Postecoglou.
While he started last term positively, his form has faded since the start of 2024 and into this term.
"I hope not. I hate how we’ve just normalized all that stuff," said Postecoglou on social media abuse driving Johnson to disable his accounts.
"I’ve been around long enough and even when I was playing, I copped a fair bit, but it was usually on the terraces and then the game was over and you’d go home. When people are at the game they get a bit frustrated that you’re not playing well, they give you some fairly direct feedback, I’ve had all that.
"You’re talking about a young guy who is probably lacking a bit of confidence at the moment. Things haven’t gone his way, but he comes here every day, he’s working his backside off, he’s asking for feedback, he’s doing everything right, he’s trying so hard to become the player he wants to be, it’s hurting him a lot.
"It’s not like he’s out on the town and he doesn’t care and he rolls up late. So what’s his crime? His crime is he isn’t performing at the level that people expect of him. As a professional footballer you've got to expect that you’re going to get criticism about that, that’s part of your growth. He’s still a young player and I think there is so much more of Brennan that we’re going to bring out in him.
"It's sad for me that we’ve kind of normalized that stuff. That getting abuse, and it is abuse and a lot of it personal, is 'oh well, that’s part of the territory'. I don’t see that."