Victory would have moved Marseille level on points at the top with defending champions Paris Saint-Germain and second-placed Monaco. But coach Roberto De Zerbi's side fell three points behind them in third place.
After left back Diego Moreira put Strasbourg ahead in the 40th minute with a left-footed drive, Marseille striker Mason Greenwood had a shot well saved by goalkeeper Djordje Petrovic.
France midfielder Adrien Rabiot came on in the 62nd for his Marseille debut after joining from Juventus.
Marseille substitute Neal Maupay's effort was saved by Petrovic, and this time there was no comeback for De Zerbi's side following last weekend's remarkable 3-2 win at Lyon.
Strasbourg coach Liam Rosenior has enjoyed a solid start and his side are in eighth spot.
Earlier Sunday, Japan forwards Keito Nakamura and Junya Ito scored first-half goals to help Reims win 3-1 at Angers and move up to fourth, two points behind Marseille.
Reims lost their opening game this season but coach Luka Elsner's side are five matches unbeaten since, and are the only team to take points off PSG in a 1-1 draw.
Nakamura put Reims ahead in the ninth minute after running onto defender Cédric Kipré's pass and Ito doubled the lead in the 25th after turning in right back Aurélio Buta's deflected cross.
Midfielder Marshall Munetsi added the third before Angers pulled back a late consolation.
Midtable Lyon rallied to win 2-1 at Toulouse, with forward Malick Fofana scoring the winner five minutes into stoppage time.
After Yann Gboho's early goal for Toulouse, an own-goal from Rasmus Nicolaisen drew Lyon level, before Fofana pounced following good work by midfielder Rayan Cherki.
Saint-Etienne rallied to draw 2-2 at Nantes.
Saint-Etienne was reeling from an 8-0 loss to Nice in the previous round and fell behind to a 10th-minute goal from midfielder Johann Lepenant, who set up forward Sorba Thomas shortly after the break.
Another heavy defeat seemed possible as Nantes then hit the post, but striker Ibrahim Sissoko struck twice for the visitors.
On Saturday, Monaco scored an injury-time winner in a 2-1 win against Montpellier and PSG beat Rennes 3-1 on Friday.
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