Celtic scored three times away from home in Europe against Real Betis on Thursday night but still came away with nothing following a 4-3 defeat in Seville.
An Anthony Ralston goal in the 87th minute revived hopes of a point but the Bhoys ultimately failed to find the equaliser in the remaining few minutes.
Hartson shares the positivity that Celtic fans have around the team and believe they are playing well at the moment despite being behind Rangers in the Scottish Premiership.
He thinks the performance against Real Betis was encouraging and the former Bhoy urged Celtic fans to continue to support Postecoglou and the team going forward.
Hartson took to Twitter and wrote: “Despite the result been a nice trip back to Seville 1st time in 18 years
“Lots of hoops fans around feeling is the team are playing very well but the need to defend better is a concern.
“Positivity and support Ange and the players.”
Celtic will look to shift their focus towards the league when they take an away trip to Livingston on Sunday afternoon.