A poor first half saw Aurelien Chedjou and Florent Balmont put Lille 2-0 up at half-time before Salomon Kalou added a third five minutes after the break.
Lisandro Lopez got one back from the penalty spot seven minutes later but the hosts could not find any further goals.
It was Les Gones' second successive defeat following the reverse against Ajaccio as their title challenge falters.
Speaking to reporters, Garde said: "We had a very bad first period. The team did not show the determination that I was expecting and that annoys me.
"The relative inexperience is an explanation. Neither the young nor the most experienced have been up to it. Nothing worked.
"I am disappointed with the lack of desire displayed.
"In terms of the game, Lille were stronger than us and deserved their victory.
"Questioning is necessary for all players as members of staff."
Lyon face Tottenham in the Europa League on Thursday and their current form, as well as conceding six goals in two games, concerns Garde ahead of such a tough match.
"The defensiveness is often the barometer of a team," he said. "This is not the game that will reassure me (before Tottenham).
"But Thursday is another competition and another context. It will be worthy of the physical challenge that awaits us."