Montpellier struck once in each half at home in Ligue 1, although Omrani's goal for Marseille in the 68th minute gave the visitors some hope of at least earning a point at Altrad Stadium.
But Marseille would finish the match with just two shots on target and their coach Bielsa argued it would have been unfair on Montpellier if his team had scored an equaliser, insisting the French league leaders were not dangerous enough in the final third.
The defeat extended Marseille's winless streak away from home to seven games in all competitions.
"After reducing the deficit, we didn't create any chances to equalise," the Argentine said.
"It was a balanced match but if we had managed to equalise it would not have been merited.
"We found it easy to get to their last line of defence but we didn't have many clear chances and we didn't manage to create any dangerous chances."
Montpellier completed a perfect season against Marseille with Friday's win, having defeated Bielsa's men 2-0 in the second round of the 2014-15 campaign.
Kevin Berigaud's strike from just outside the area put the hosts in front after 35 minutes, while Paul Lasne doubled Montpellier's advantage in the 62nd minute after a defensive mix-up allowed Anthony Mounier to tee-up his fellow midfielder.
Omrani equalised just six minutes later with a sharp volley at the back post, following Brice Dja Djedje's cross but the 21-year-old forward conceded his first senior goal for Marseille was overshadowed by the loss.
"The joy at scoring my first goal for OM [Marseille] is spoiled by the final result," he said.
"But it is still a source of pleasure to score my first goal for Marseille. I would have liked us to win the game but it wasn't to be.
"Every team is better in front of their own fans but we will try to start getting results away from home."
Marseille's loss could see them fall from first position for the first time since round five this season.
The leaders have 41 points and plus 20 goal difference but could drop as low as third if Lyon (39, plus 23) defeat Toulouse on Sunday, while Paris Saint-Germain (38, plus 19), who are third, could also overhaul Marseille if they win by two goals at Bastia on Saturday.
