The result sees Spurs finish in the top eight after the group phase.
Postecoglou said: "I'm super pleased. The objective today was obviously to win the game and finish in the top eight, and we knew we were going to have to rely on the young brigade. I thought they stood up really well; the whole group did. We controlled the game, we just had to be patient because Elfsborg sat really deep, and I thought we maintained our composure and got a good win.
"I think the club are especially proud of the youngsters – the academy coaches and players who would have been cheering them on tonight. They are three young boys who have come through, made in Tottenham, and credit to them. We had to rely on them as we've got a big week coming up and they stood up.
"This competition is massive for us. By the time we get to the round of 16, we'll hopefully have some of our injured players back and that will give us a good crack at it. We've put ourselves in a really good position by skipping the play-offs, which gives us a couple of extra weeks, and I'm looking forward to it."