Gillot's men have won once in five league games so far in 2013-14 and fell to a 3-0 defeat against Eintracht Frankfurt in the UEFA Europa League on Thursday.
The 53-year-old - who has been in charge since June 2011 - has seen Bordeaux lose their last three matches in all competitions, conceding seven goals in the process.
"I am very worried for the future," he told L'Equipe. "Not only for Europe but also for the Championship, I worry a lot.
"Some had the opportunity (against Frankfurt) to show and they did not. They did not show anything.
"We are not effective in both areas (attack and defence), this means that there are no effective players.
"We have a lot of work to do."
Bordeaux return to league action on Sunday when they travel to Lorient.
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