Spurs won 3-1 via goals from Brennan Johnson, James Maddison and Dominic Solanke. However, Ulrik Saltnes struck late to give the visitors hope for the second-leg.
Postecoglou said afterwards: "Yeah, I think it puts us in a good position. I thought the players were outstanding today, I thought our performance was everything it needed to be, really well organized and disciplined defensively and really calm going forward and created good opportunities for ourselves and maintaining pressure.
"Obviously they scored the goal late, which doesn't I think reflect our dominance in the game, but if we repeat that performance next week and it'll be enough for us to get through.
"I thought our supporters were outstanding tonight, from the moment we walked out and I think they added the energy to the team. Even us scoring an early goal came from the fact that as soon as the boys walked out, there was a buzz in the stadium and that's a credit to our fans.
"We've obviously had a tough season, but the European nights this year have still been pretty special and they played their part tonight, massive role in us performing in the way we needed to."
"I know all about Bodo/Glimt's artificial grass"
Spurs will go to Bodo/Glimt needing to navigate their plastic pitch, with the Norwegians also aiming to make the most of their late goal scored.
Postecoglou continued: "Yeah, look it is on artificial grass but it’s still a game of football. I’ve been there, played there with Celtic, I know the experience and what is important for us is we need to replicate what we did today.
"Irrespective of the surface, if we’re as disciplined and as organised as we were today, with and without the ball, it won’t matter what the surface is, I think it will make it really difficult for us to be stopped."
Asked if there was a disappointment about conceding late, Postecoglou said: "Yeah look I thought we were similarly dominant against Frankfurt you know and we ended up with 1-1 there, but I think when you perform like we did tonight and like we did against Frankfurt at home, it gives you that belief that you can go away and win there as well.
"I think that is the most important thing. I certainly don’t think the scoreline reflects our dominance in the game today, but we have to accept that. We’re still in a really good position and it’s about now replicating what we did today on Thursday."