Goals from Jota and David Turnbull helped Parkhead’s side secure back-to-back Premiership wins on the road as they shed their hoodoo of the day away from home.
Coupled with Hearts’ late leveling against Rangers, this narrows the gap between rivals Glasgow to four points.
Postecoglou was quick to strike back at critics who have already written his side in the Premiership title photo after reaching top form in Lanarkshire.
When asked if the Ranger drop points were ‘the icing on the cake’ for Celtic, Postecoglou joked: ‘Well I thought the Premiership race was over, mate, so I didn’t watch. plus the table.
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“We’re kind of doing our own thing and it doesn’t matter to us.
“I think what’s most important for us is that we have confidence in ourselves today. It’s one thing to get a win here, but controlling the game like we did today should give the boys some real conviction.
“There are big games starting on Tuesday so I think that’s the main thing for us.
“We’re just going to keep doing our own thing and see where we end up. “
Postecoglou hoped the second road win this quarter would prove to be a turning point for the team,
He noted the instant impact of Giorgos Giakoumakis, Mikey Johnston and Nir Bitton on the game as his injuries continue to ease.
He told the BBC: “For us, and me in particular, the turning point is that we are just more settled now.
“As you saw today, we were able to put in place three players who can make an impact in the game.
“We still have players outside the squad who can make an impact.
“We have big tasks ahead of us, starting Tuesday.
“But for us it’s just a lot more settled and I think the players and I are more comfortable with it. “