Kinsky has quickly established himself at Spurs, having only arrived last week from Slavia Prague.
The youngster is yet to be beaten in Cup victories against Liverpool and Tamworth.
"It’s a different challenge but it’s more to do with mindset in that he’s prepared to embrace that challenge, and the challenge we found in the last game when we found out just how strong they are on offensive set pieces and the players they’ve got in terms of both delivery and execution," said Postecoglou.
"You need to be well organised but you also need your goalkeeper to play a pivotal role. So far what I’ve seen of him he’s embraced those challenges. It’s not easy going to a place like Tamworth and they’re throwing balls literally under the crossbar and you’ve got about 20 bodies around you, and as much as it’s about technical ability its more about mindset and tackling that and he didn’t shy away from it.
"That really helped us because it gives confidence to the players around him because they know if it’s in his area he’s going to come for it and they can focus on their job."
The Australian also said: "It happens with almost every new player but particularly a key position like goalkeeper. It does give some comfort to the players around him if they see he’s handling it well. It means they can then focus on their own job and be a lot more clear-headed.
"If he was struggling to adapt to the way we want to play or challenges... We prepared for Tamworth and what they were going to do, we knew every time they had a throw-in in our half it was going to come in the box and how we’d want to deal with it. That’s great in theory but then you have to go do it.
"When he came out and dealt with the first two and caught them, the players around saw that he’s got this. 'If he’s got this, I’m going to make sure.' If he didn’t and there was uncertainty there it tends to filter through the whole team."