He was photographed crying on the bench after being taken off 71 minutes into Brazil's 5-1 thrashing of Bolivia in a 2026 World Cup qualifier in Belem.
Richarlison, who has scored only four goals in 40 games for Spurs, told Brazilian newspaper O Globo after the game that he would consult a psychologist "to come back stronger".
"Whatever Richy needs, we'll help him get to the space he wants to. He was emotional after a game and that's fine," Postecoglou told reporters ahead of Saturday's Premier League game at home to Sheffield United.
"We'll provide all the support he needs. I'm sure every player in the dressing room is dealing with something.
"There's always something that isn't where you want it to be. It's about keeping perspective and balance. That's part of life."
Postecoglou also praised James Maddison's impact, with the England midfielder named Premier League Player of the Month for August after two goals and two assists in four games since joining Spurs from Leicester City for a reported fee of 40 million pounds.
"It was a fairly low-risk acquisition because of his quality. But the way he's embraced the club, on and off the field, has been fantastic," Postecoglou said.
"You're looking for enthusiasm and freshness and he's created a real good energy around the place."
After failing to qualify for Europe last season, Spurs look like a team reborn under new manager Postecoglou and are playing with a high-tempo style that has propelled them to second in the standings with three wins and a draw from four games.
"We've had a promising start. I didn't go into it with any kind of expectations," the Australian said.
"Embedding a style of play into the group was the key thing for me. We could be sitting on 10 points but if we hadn't been playing our style of football, I wouldn't have been comfortable. We're only a month into a long season."
Spurs' next opponents 17th-placed Sheffield United have taken one point from their first four games after promotion.
