The midfielder moved to the Stade Velodrome in September from Lille and has started 19 games in Ligue 1 as Marseille battled to get into the top three.
Much was expected of the 21-year-old after impressive campaigns with Bastia in the last two seasons, but his performance levels have dropped in recent weeks to prompt some criticism.
Anigo admits the youngster has not been at his best, but has called for patience with the France Under-21 international, who left Lille in acrimonious circumstances without playing a game for the club.
"There is no problem with Florian," he told L'Equipe. "Simply, he is having a bad time right now.
"But remember he did not have pre-season preparation for the reasons we know, and today he pays for it.
"He is only 21, we must give him time to grow slowly."
Thauvin has scored six league goals for Marseille this season and is the highest-scoring midfielder within Anigo's squad.
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