“The fact that they’ve got to limit their world, close their world a little bit because of… I mean what kind of person writes abusive things to an individual?” he added.
“Criticism is one thing, exasperation at a game, you accept that. To sit down and write something abusive anonymously… say it in front of me, you’ll get a punch on the nose, you won’t do it again, mate. But they won’t do that.”
Postecoglou, whose side are 13th in the early-season table, could include Johnson when Tottenham go to Coventry City in the EFL Cup on Wednesday.
“When I look at Brennan and I see a young man who is trying his hardest to be the best he can be,” he said.
“It doesn’t always guarantee success and it’s part of his journey how he deals with all this. But he’s a great kid, a great footballer and I’m very optimistic about what he’s going to do for us.”