Rangers’ performances have been poor for a while, but tensions at Ibrox reached fever pitch when they dropped points against Livingston last Saturday.
The team were jeered off the pitch by the home fans and Van Bronckhorst was the subject of unhappiness from a large section of the Rangers supporters.
A section of the Rangers fans are now prepared to see the Dutchman be sacked, but Hartson feels the supporters are being too harsh towards the manager at this point of the season.
He pointed out that Van Bronckhorst led them to the Europa League final and Rangers are still very much in the title race.
The former striker does not feel he deserves the poor treatment being meted out to him and believes it is too early to call for his head.
Former top flight striker Hartson said on the Go Radio Football Show: “For me, Giovanni van Bronckhorst took you to the Europa League final.
“Before the weekend, you were only two points behind Celtic in the league who have had the second-best start to a season in so many years.
“And all of a sudden a draw at home and you want the manager out? Who would you bring in if Rangers did?
“I know he is getting a lot of stick and I saw some of the videos and some of the fans shouting and howling at the manager at the weekend, does he really deserve this?
“The Champions League is a different level, you have got to step up in terms of miles to get results against Liverpool, Napoli and Ajax.
“These are European giants so I still think it’s a bit harsh calling for his head, I really do.”
Van Bronckhorst will hope to get the Rangers fans back on his side when Ibrox hosts Aberdeen next weekend.
