The military club claimed a 1-0 home victory over the Algerian outfit to book their place in the CAF Confederation Cup third round after the first leg ended goalless.
They squandered a host of chances to put the result beyond doubt and their wastefulness almost cost them the victory.
Al-Hodoud needed a superb save from Cameroonian keeper Mathurin Kameni to deny Mouloudia's Abdelmalek Cherrad from close range and preserve the team's lead.
Difficult Match
"The match was very difficult and it became even harder when we scored the opener," Al-Ashri told Modern TV after the match.
"Any goal for Moloudia would have thrown us out of the competition."
Al-Hodoud striker Abdul-Hamid Bassiouni assisted Mohamed Al-Herda's goal but wasted some clear-cut chances. Al-Ashri still backs him.
"Bassiouni is going through a dry spell because of his bad luck. I'm sure he will soon rediscover his scoring touch."