Garde saw his side thrashed 5-1 at Montpellier over the weekend and the result left Lyon 14th in the Ligue 1 table after nine games, 10 points adrift of the leaders.
The club also failed to qualify for the group phase of this season's UEFA Champions League after losing to Real Sociedad in the play-offs.
Questions have been raised over Garde's future and the former Arsenal midfielder is aware it is the most difficult period of his tenure.
"Resignation? I know that is the kind of latest fashion question to be asked of some of us [coaches], but I don't think about it at all," Garde, who took charge of Lyon in 2011, said after the defeat by Montpellier.
"However, I have been asked if I feel in danger and the reply is yes, I feel under threat considering the results.
"We have already played almost a quarter of Le Championnat and we are far away from what we can achieve.
"Is it the most difficult period since I have been coach? Yes, clearly. A crisis? I will let you use whatever word you want - crisis, ruin, etc.
"I know the period is difficult for the club because one win in 10 matches is clearly not enough."