Johor took the lead in the 17th minute when captain Safiq Rahim set up Luciano Figueroa, who slotted the ball past Kitchee goalkeeper Wang Zhenpeng.
The Malaysian side doubled their lead just before half-time when Rahim converted a penalty after Subramaniam Kunalan was brought down inside the box.
But, Tarres admitted that his side were lucky not to concede four goals in the first half.
Despite an improved performance in the second, Kitchee were unable to cut Johor's lead down and have now been overtaken by the Malaysian side on the Group F standings.
Kitchee must now win their next two matches if they want to qualify for the knockout stage of the tournament.
"If we want to qualify, we must win our two remaining matches," Tarres told the South China Morning Post. "We have the quality but we must prove it."
Meanwhile, Kitchee head coach Jose Molina attributed his side's loss to their less than impressive performance in the first half.
"We didn’t play well and lost control of the game in the first half," he told the-afc.com. "The second half saw us perform better after we regrouped but it was too late to get anything out of this game."