The Bhoys lie bottom of their Champions League group after four matches with just one point and have a tall task on their hands if they are to qualify for the knockout stages.
Celtic can go some way towards getting an unlikely qualification to the knockout stages by defeating Shakhtar Donetsk when they meet in the penultimate group stage round later in the month.
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Hartson thinks that the harsh nature of football means Celtic do not have much to show for in terms of points, but it obscures how much effort the Hoops have put in.
The Celtic legend insists that the Hoops will have to score much more when they take on Shakhtar Donetsk but fancies his former team’s chances on the night.
Speaking on the Go Radio Football Show, Hartson said: “Football’s really harsh, you get nothing for not playing particularly well or conceding goals.
“But I think the effort level’s been there, they could have scored goals in every single game.
“They have only scored two and I think that’s going to have to change against Shakhtar.
“I really fancy Celtic in two weeks’ time.”
With a top two finish in the group now unlikely, Celtic will be keen to at least grab the Europa League spot by finishing third.