Following a 1-0 loss to Sevastopol on Wednesday, goals from Florin Costea and Pantelis Kapetanos condemned Neil Lennon's side to another defeat in their pre-season preparations
Neil Lennon's side hit their first goal of pre-season through Georgios Samaras in a difficult encounter against the Romanian side, which offered a marginal improvement on their 1-0 loss to Sevastopol last Wednesday.
Cluj have already played a number of friendlies and begin their domestic campaign on July 20, so it was of little surprise when they went 2-0 up with goals from Florin Costea and Pantelis Kapetanos.
The Romanians displayed their superiority early on by going ahead after just nine minutes.
There was little that Celtic goalkeeper Fraser Forster could do when former St Johnstone and Inverness forward Gregory Tade played in Florin Costea, who sent a curling effort into the top corner.
Cluj dominated the opening exchanges, but Kris Commons almost brought the Scottish champions level shortly before the break when his free-kick was palmed away.
Lennon made three changes at the break but the substitutions could not bring them the equaliser, and Cluj added to their woes in the 64th minute when Kapetanos finished well after finding himself in a great position in the box.
Celtic did mount something of a challenge in the 71st minute, but James Forrest could only fire over the bar.
The Glasgow side - who face Cliftonville in the second qualifying round of the Uefa Champions League later this month - continued to improve in the second half and got themselves back into the game when Forrest’s cross came off the knee of Samaras and into the net nine minutes from the end.
However, the Greece international's strike was a case of too little, too late for Celtic, who have now lost both their games on their pre-season tour.