The southern French club suffered their fifth straight defeat in all competitions on Saturday with Reims claiming a shock 3-2 win at Marseille's Stade Velodrome.
Marseille came from two goals down at half-time to equalise with four minutes to play but a stoppage-time header from Prince Oniangue handed the visitors victory and increased the pressure on Baup.
Despite the result, Marseille's sporting director Jose Anigo argued the club remain confident Baup can turn the nine-time French league champions' form around.
"(Baup) is supported by everyone and we have a constant dialogue," Anigo said.
"He must be able to work calmly."
Marseille's president Labrune Vincent was similarly supportive of Baup.
"We are together and together we will find solutions to get out of this," Vincent told L'Equipe.
Saturday's result saw Marseille slip to sixth in Ligue 1, seven points behind leaders Paris Saint-Germain, who have a game in hand.
"We all realise we are in a difficult situation," Mandanda said.
"We all need to be more committed and stand together but I believe in this team."
