Barton received his marching orders just after the hour mark for his second bookable offence, although Baup believes that the decision was harsh.
"I'm saying this in the heat of the moment, but this is a big blow, and the performance was not what we hoped for," Ligue1.com quotes Baup as saying.
"We tried to play an attacking game, but the Barton sending-off was the turning point.
"Barton didn't deserve to be sent off. We used two tactical systems and couldn't find the solution. We have conceded too many goals from corners this season."
Marseille are now six points behind Ligue 1 leaders Paris Saint-Germain.