The Hoops began the defence of their title with a 2-0 win at home versus Aberdeen courtesy of goals from Stephen Welsh and Jota.
They then beat Ross County 3-1 away on Saturday, with late goals from new signing Moritz Jenz and Liel Abada securing the three points.
Up next for the Bhoys is a challenging fixture against Kilmarnock away, with Postecoglou postulating difficulties courtesy of the artificial surface at Rugby Park.
Postecoglou paid tribute to Killie coach Derek McInnes for his part in their promotion last year and believes that their next opponents will look to prevent them from getting into their stride.
Despite the challenges accompanying playing on the artificial surface, the 56-year-old tactician emphasised that the solutions are to be found in staying true to their brand of football.
“Every week’s a different challenge and this will be a different one”, Postecoglou told Celtic TV.
“They got promoted last year and Derek McInnes did a good job to get them up and I’m sure they will be looking forward to these fixtures and seeing if they can disrupt and stop us.
“Playing at their venue is another challenge on an artificial surface which affects our game, so all those things are there but whatever challenge there is, the answer lies in our football and as long as we concentrate on playing our brand of football and believing in it we will be fine.”
Celtic currently top the Scottish Premiership table after a pair of fixtures, ahead of rivals Rangers on goal difference.
