Sixth place in the cinch SPFL Premiership after six games played – a healthy goal difference of 12 yet only nine points to speak of, all gathered at home, is an enigmatic start to the manager’s reign at Parkhead.
But away concerns aside, Hartson isn’t hitting the panic button – and is pleased the fans are sticking with the manager through the current, turbulent, league form.
"I think there were about 5,000 Celtic fans [on Sunday] and I think a lot of people realise it is a bedding in period.
"Rangers are huge favourites considering they won the league by 25 points, kept every single player from last season almost, haven’t sold anybody.
"There were about 10 who left Celtic, 12 who have come in, there is a new manager, I think he has done very well.
"He has united the crowd, he has united the dressing room in terms of where it was last season.
"Naturally, at some stage, as we go along, Celtic will have to prove that they are good enough to go and win the big games.”
Livingston away is not usually described as one, however with Rangers dropping points at home to Motherwell, an opportunity to close the gap at the top was missed as the hosts took theirs to move off the foot of the league.
The more games that are lost, or not won, the bigger the next becomes, such is the life and demands of an Old Firm manager.
“The issue is it’s big game after big game. There is no respite. He needs a stronger squad.
"We have seen he has put a team together in the last couple of games and it has not quite been strong enough to cope. He will want to add. When he gets his best players back we will see better performances again.
Until then Hartson believes Postecoglou will shut out the noise of online criticism, and he was heartened by the response to the West Lothian setback and has optimism that, given time, the team the Celtic manager has brought together, will click.
“Naturally when you don’t win there is a tinge of disappointment, especially when Rangers drop points as well.
"There were no boos from the crowd [on Sunday], which is good, they are getting behind the manager. I think that is the right thing to do at the minute – back the manager, back the players.
“I don’t think the boos will come. The fans realise it’s going to take time – and the manager will get time.”
He added: “He needs at least another window. We can’t put him under pressure after six league games. This club lost the league by 25 points last season and there’s been huge turnover.
“You look at the AC Milan game last season and Real Betis the other night. Albian Ajeti was the only player still in the side from last year and he was on the bench. It’s an entirely new team and it takes time to gel.”
John Hartson was speaking at The John Hartson Foundation Golf Day at Turnberry. The Hartson Foundation supports various cancer charities around the UK.