The current World title-holder lost to Rafael Aghayev of Azerbaijan 3-0 in a tight semi-final at the Male Kumite -75kg of Karate 1-Premier League Dubai.
Askari earned a place at the Olympics after standing first at the weight class ranking with 7702 points.
Competition will continue on Saturday in the United Arab Emirates city, with the medal bouts taking place on Sunday (February 16).
The event in Dubai is one of the last competitions before the Olympic qualification process ends on April 6.