Salomon Kalou struck a hat-trick, including twice from the penalty spot, as Lille claimed the hard-fought win to remain third in Ligue 1 on Sunday.
Girard was unhappy with Lille's display and was stunned they somehow managed to collect an important three points.
"We were very poor. We just never got going. Ajaccio surprised us and posed us serious problems," he said.
"We knew that Ajaccio were condemned to Ligue 2 but the team showed that they want to finish the season well.
"We were chasing the game initially but we never managed to get a foot on the ball and make the play. It really is a miracle that we won it."
Kalou cancelled out Gadji Tallo's early goal before putting Lille ahead with his 38th-minute effort.
But it was 2-2 at half-time when Tallo scored once more, only for Kalou to respond with what proved to be the winner from the penalty spot on 74 minutes.
Adama Soumaoro was sent off for Lille with eight minutes remaining, but the visitors held on.
Kalou said: "I scored three goals but for me the essential thing was the victory. We had to get third place back after Saint-Etienne's win against Monaco.
"We have been struggling recently, perhaps due to the number of matches we've had to play.
"We were surprised by their start to the match. They pressed us high up the pitch and the early opening goal changed the game.
"We were lucky to be level at the break and we corrected certain things in the second half that allowed us to take control of the match.
"It was a painful victory but it allows us to get third place back."
