The second half saw the Gaurs create more chances than Al Zawraa, although their finishing mostly failed to test the goalkeeper and left a lot to be desired.
A Borja Herrera cross into the box from the right found Javier Siverio but the Spanish forward’s acrobatic attempt lacked the power to threaten the opposition goal.
As the half wore on, FC Goa pushed more players forward in search of an equaliser and created numerous chances from open play and set-pieces without ever managing to apply the finishing touch.
The Gaurs also rode their luck as Al Zawraa hit the woodwork for the second time in the match during the last minute of regulation time.
The reprieve gave the hosts one last chance to get an equaliser as Javier Siverio had another headed opportunity in the fifth minute of injury time but failed to hit the target yet again.
Soon after Siverio’s miss, Al Zawraa put the game to bed after Nizar Al Rashdan managed to squeeze his shot through a host of legs and beat the goalkeeper to make it 2-0 as the Gaurs began their AFC Champions League Two campaign with a defeat.
FC Goa will face Tajikistan’s FC Istiklol in their next Group D encounter on October 1.
Organised by the Asian Football Confederation (AFC), the ACL 2 is the continent’s second-tier club football competition, a rung below the AFC Champions League Elite. Sharjah FC of the UAE lifted the inaugural title last season.