The Australian was doubly delighted as he watched his side record another clean-sheet with the win, having done the same against Ferencvaros in the UEFA Cup last Wednesday (AEDT) and away at Motherwell in the league last weekend.
Celtic now sits fourth on the table with 19 points from 10 matches, but it is just one point adrift of the top three, all of which have 20 points, although Rangers could pull clear if it claims three points from its trip to St Mirren on Sunday.
"We didn’t expect it to be an easy game, they are well organised and they work hard, particularly defensively and we had to be patient and keep our discipline," Postecoglou said.
"But I thought we did that well. We didn’t really get too anxious about things, we moved the ball around and we created the chances we needed, so we took them at the right time, and in the end it was a deserved victory.
"[The first goal] was good, in these kind of games you have to take your chances because you know you’re not going to get a lot of them. There’s not going to be a lot of space, particularly in and around the box the way they play.
"So it was never going to be a game where we could open them up, and it was a bit of a lucky bounce.
"But that’s what we work on, anything that breaks in those areas, getting the first ball across and Giako was there to do the job."
Postecoglou also highlighted the discipline in the performance, particularly at the back.
"That’s going to be important for us in games where we dominate," he said.
‘Sometimes we won’t have the scoreline domination, so we’ve just got to keep things tight and make sure we play the game in their half."