Spurs won 2-0 thanks to an own goal and Pape Sarr to ease pressure on Postecoglou.
He said afterwards, "It is a difficult place to come and win at.
"It’s also a difficult place to win with the way they attack and set up; you have to defend your box. You’re just going to have to do that.
"I thought the lads handled that awfully well and we knew it was going to be key for us and the lads were brilliant and we felt we had the quality of football to hurt them the other way. Credit to the boys, they were brilliant."
On man-of-the-match Djed Spence, Postecoglou added: "Since he came into the team he has been outstanding.
"We missed him the last couple of games but that's the beauty of where we're at at the moment. We're slowly getting players back, improving us and helping us and I think that's giving energy to the group. He was great today."