The Parkhead side closed the gap to rivals Rangers to two points with the 2-0 win over Motherwell at Fir Park.
Jota and David Turnbull scored either side of the interval to hand Celtic their second successive away success.
Postecoglou refused to pay attention to what happened at Ibrox as Rangers drew 1-1 with Hearts.
“I thought the Premiership was over so I’m not looking at the table any more,” he said.
“We are just doing our own thing so that result has zero significance. What’s more important to us is that we get more belief into the team. It’s one thing to get a victory here but to control the game should give the boys real belief and confidence moving forward.
“The main thing for us is to keep our heads down and run our own race.”
Celtic controlled the game for large periods and looked confident doing so which pleased Postecoglou the most.
“We’ve been making steps forward, we are a lot more settled,” he said. “All of the players have been here now for at least one month so we’re not throwing them in.
“We’re not giving guys debuts and everyone is a bit more comfortable and they all want to play.
“We are just beginning and whatever we do now, I know we will be better.
“We are beginning to see a foundation for what we are trying to build. That doesn’t excuse us not winning games. I know that we will be a much better team as the season goes on.
"The players will get even more understanding and belief in what we are trying to do.”
Two Celtic stars earned the praise of their boss for their influence.
“The side worked hard but it was Tom Rogic who was providing that X factor which we needed.
“David took that over in the second half but I was pleased that he got his goal and his general all-round play was good.
“Tom finds space when we need it and the game is tight and physical. He’s just one of those players where the game slows down when the ball is at his feet.”