While Lille sit third in Ligue 1, Auxerre have been finding the going tough in the second tier this season, currently occupying 14th place.
Girard had several regulars unavailable for Tuesday night's match, and chose to bring in others battling to break into his preferred XI.
But those who came in from the cold are set to slink back into the background after flopping badly.
Girard said: "In football, you have to dig deep to win. We could have played for three hours and I don't know if we would have been able to score. We played a lacklustre first half and despite everything we had chances to open the scoring.
"There were a few lads who weren't involved - those who are injured and suspended - and others who were knocking on the door to play.
"Some of them were lacking game time and therefore they also lacked the fluidity we hoped for.
"These players had to show what they could do. We shouldn't condemn them, you can't find rhythm easily.
"On the other hand, they have to do better to hope to knock at the door and get in front of others. They need to be aware that the level is very high.
"We only have 21 players and I thought those I selected were capable of getting a good result."
Sebastien Haller scored the only goal of the game for the Ligue 2 outfit with seven minutes of extra-time remaining.
Bernard Casoni, the Auxerre head coach, said: "This is a reward for all our efforts. We stayed well organised and consistent to the end.
"It's not an undeserved victory. Even if we conceded a lot of corners against a good Lille team that had a lot of players missing, we managed to raise our level of play.
"We had already given good performances at Caen and Brest in the Coupe de la Ligue and here we have beaten Lille, who have been on a very good run, so it's very interesting."