Celtic dropped more points away from home on Sunday when they suffered a 1-0 defeat at Livingston.
The Bhoys have not won a league game on the road since February and are currently sitting sixth in the Scottish Premiership standings, four points behind league leaders Rangers.
It is Celtic’s worst start to a league campaign in 23 years, but Hartson stressed that the time is still not right for the club to hit the panic button just yet.
He believes manager Ange Postecoglou still has the support of the Celtic faithful and pointed out that his job is to rebuild the squad after a dreadful last season and summer of a few top players leaving the club.
Hartson also stressed that despite their poor start to the season, Celtic are still just four points behind Rangers and it is too early in the season to pass any judgements.
The former Bhoy said on the Go Radio Football Show: “I think with Ange there will be no panic settling in at the minute at Celtic.
“The crowd is still with him, his blueprint at the start of the season when he came in was to build a new team.
“He has got several key players out and at this moment in time, they are having a poor run away from home.
“Yes, they will want to start winning but they are only four points behind with six games gone and so it’s very early.
“As I said, I don’t think it is time to panic just yet.”
Celtic will look to reach the semi-finals of the Scottish League Cup when they take on Raith Rovers on Thursday evening.