Spurs meet Aston Villa on Sunday.
Postecoglou said of Emery: "Yeah, great appointment. But it shouldn't surprise anyone, he was an outstanding manager before he got there.
"He's done an outstanding job and another cautionary tale about writing people off because when he was at Arsenal, people were quick to be dismissive of him. Lots of other people's memories have faded.
"When you're a manager and you see a manager going through what he did, it's firmly imprinted in your mind; just goes to show, as I said, he was an outstanding manager and for Villa, they identified somebody that could come in and really bring their football club to the levels they wanted to, and he's done that. Since he's been there they continue to get stronger and challenge and it'll be a good test for us.
"Our games against them have been really good. Last year, we won at their place and played really well but I thought we played well at our place too but they got on top of us, they got ahead of us for the Champions League last year. It's great competition for us."