The Iraq League champions are languishing at the bottom of Group D with two points, eight less than leaders Kuwait’s Al Qadsia.
Salman, who guided Iraq in the 2007 Gulf Cup before taking over the reins of Arbil, said: "I can’t continue in my current job after such a heavy defeat, which I am partially responsible for."
Under Salman, Arbil won their first-ever league title last year and the team has already made their way into the elite level in the league this year.
Meanwhile, the club has appointed former Al Zawra and Al Quwa Al Jawiya tactician Saleh Radhi as their new coach. Radhi led Al Zawra to the 2005 league crown before moving to Lebanon’s Al Mabarrah.
Radhi’s first challenge at the continental level will be against Qatar’s Al Gharafa in the AFC Champions League on May 7.