Abdulrahman was chosen to be Jaime Pacheco's successor after the latter was sacked following Al Shabab's disappointing run of form in the Saudi league.
Al Shabab, who beat Al-Faisaly 2-1 in their Saudi Professional League match on Friday, are currently sitting last in the Group B standings.
The match against Naft Tehran will be a good test of Abdulrahman's character as Waleed Abdullah, Hassan Raghfawi and Amer Harun are all unavailable.
Abdullah will be out the remainder of the season after undergoing knee surgery, Raghfawi is still recovering from a foot injury and Harun has been suspended.
Despite this, Abdulrahman has called on his side to avenge their 2-1 loss to Naft Tehran on March 18.
"The match against Naft Tehran will be decisive for us in the AFC Champions League," Abdulrahman told the official AFC website. "The match will determine our fate in the competition and hopefully we can have a good result and maintain our chances in the group.
"We will try our best to take advantage of playing at home and in front of our fans to get the positive result. We have prepared well and I'm confident that the players will give all their best in order to achieve the result that we are looking for."