The Celts moved five points clear at the top of the Scottish Premiership table after thrashing Rangers 4-0 in the first Old Firm derby of the season.
Celtic have been ruthless in the Premiership, having won all six of their games, scoring 25 goals in the process and conceding just once.
Looking ahead to the Champions League clash with defending European champions Real Madrid, Postecoglou said: "Now we'll get ready for Tuesday night. They're an unbelievable team with outstanding pedigree.
"They're champions of Europe but we'll go out there and test ourselves.
"We don't need motivation to raise our game. If you go to Ross County and score four, you need to be motivated or you slip up.
"To score nine last week and break a record, you need to be motivated. We were motivated today and we'll be motivated on Tuesday night.
"We don't need to change our approach to measure ourselves against the best.
"We'll get really tested against Madrid but that's what we want. You've got to respect the opposition. They're a top team.
"But what we can control is what we bring. We'll give our best, our way. That's the key. This is who we are now as a team and we won't change our approach.
"I've always felt the way to do that is by being yourself. We have to bring our own identity - that's the approach we will take.
"What a great opportunity to play our football. If we're not successful, we are not successful.
"But let's go down swinging rather than deferring to someone because they're a good team and changing our approach.
"Our supporters want us to take the game to Real Madrid and see where it takes us. Let's have a crack anyway."