Courts has made a promising start to his United reign after stepping up from a role in the academy in the summer, and his side will travel to Celtic Park on Sunday one place and one point above their hosts in the cinch Premiership.
United had a setback in midweek when they lost to Hibernian in the Premier Sports Cup but Postecoglou, who is having his own challenges, stressed that such experiments are never instant successes.
The former Australia head coach said: "I like clubs who do things a little bit differently and try and head off in a different direction.
"The test comes when it doesn't go smoothly, and it never goes smoothly to start with, irrespective of which direction you are going in.
"If you really want to change things in a significant way, then you have got to expect things to be rough at the start.
"If you play through that and stick to your beliefs, and you have got the right person, it will bear fruit.
"He is just starting on his managerial journey and good on him for trying to do things a little differently."
Defeat at Livingston last weekend left Celtic in sixth place, having lost all three away matches.
Home games have not been a problem – Celtic have scored 26 goals in seven successive wins – but Postecoglou has been hit with a shortage of attacking players.
Postecoglou knows there is little room for error following their latest slip-up at Livi.
"Irrespective of who we are playing on Sunday, it becomes a really important game for us, particularly after losing last week," he said.
"We know we can't lose too many games in the league and we need to go on a run of results.
"There is no better place for it to start than at home – our home form has been really strong all season.
"Dundee United will be a tough challenge. They played on Thursday night as well which is good because we are facing a team short on preparation time.
"Hopefully we can recover well and get ready to go."