While the non-leagues pushed Spurs into extra-time, Postecoglou says the experience was a positive for new goalkeeper Antonin Kinsky and young midfielder Mickey Moore.
On Kinsky, he said: "Yeah yeah, it was a good challenge for him. That's one of the unique things about Tamworth because every time they get into your half the ball gets into your box whether it's a throw-in or free-kick, that's where it ends up. You have to defend in your box. It doesn't matter how well you try to keep them away even with a throw from the halfway line.
"I thought Toni and all the lads handled it really well because it's always a bit of a lottery when it comes in, particularly with the way they launch it. It was good for Toni to get through that."
On Moore's playing return, he also stated: "Yeah brilliant, great to get him some game time. I think he's itching to get back as well. He's missed a fair bit of football. It just adds another attacking threat to us and I'm sure after today he'll feel a lot better. As I said, I think he was a bit rusty at the start but he definitely grew into the game."
Meanwhile, on the scrapping of FA Cup replays, which has cost Tamworth a replay at Spurs, the Australian added: "I get the sentiment but at the same time I have been banging on about less games so it is a balancing act. The way the calendar is at the moment it would be almost impossible for us to fit another game in.
"We are already struggling to fit it all in. I understand the sentiment around it and I certainly believe in the competition and what it does offer every part of the football pyramid and I think it should be protected."