Anigo was chosen to take over from Elie Baup at the Stade Velodrome in December and has hinted he could remain in charge for the rest of the season.
Gignac, the scorer of nine goals in his last eight games, has revealed Anigo has given him confidence and adopted the right system for his strengths.
"He asked me to take more responsibility on and off the field," Gignac told L'Equipe.
"I am confident. In addition, I blossom in the 4-4-2 (system). I am never lonely."
Anigo's men were beaten 2-0 by Monaco on Sunday but have the opportunity to move up to fifth in the league with victory against Valenciennes on Wednesday.
Gignac is confident Marseille can bounce back but feels defensive improvements are necessary.
"We created a lot of chances (against Monaco) but it leaves holes in defence. It is this imbalance that we need to get (right)," he added.
"(Valenciennes) is a pivotal game. We can get back in the race (for European qualification), I firmly believe."
