The fullback penned a new deal to 2028 in midweek.
Postecoglou said on Friday: "I said a couple of days ago and consistently say, most of a players future is in their own hands. They're as much in control as anyone else. I think sometimes footballers forget that. With Djed, it could have been easy for to go out on loan again. But when he came into pre-season, he was determined to make a career for himself here at Tottenham rather than wait to be loaned out.
"He did everything right in training, his attitude was great. He's a good footballer, I think the way we play suits him and he's knuckled down to that. And he's earned himself a spot on the roster in our squad.
"The rest is up to him again. Because it's an easy decision for me to make when I see that. Like I said, sometimes footballers think their fate is in other peoples' hands. For the most part, it's in their own. If they're doing well and doing everything right, the future tends to take care of itself, whether that's where you currently are or you move on. And Djed's certainly done that."