Girard's men were forced to share the spoils after Wahbi Khazri salvaged a 1-1 draw for mid-table outfit Bastia in Ligue 1 action at the Stade Armand Cesari on Friday.
A win would have ensured Lille's place in the qualifying round of Europe's premier club competition but the third-placed team must wait a week, unless nearest rivals Saint-Etienne, who are eight points adrift, fail to beat Montpellier on Sunday.
Lille were on track to clinch a Champions League spot after former Chelsea striker Salomon Kalou opened the scoring on the half-hour mark following a swift counter-attacking move.
However, Lille were made to pay as Khazri found the back of the net from close range with five minutes remaining, which clearly aggrieved Girard.
"We must kill this match! The game is lost on our lack of lucidity offensively," said the 60-year-old.
"We have three opportunities (very close to) the line and you do not score! We could have lost the game in a completely ludicrous scenario.
"In football, you have to be focused from the beginning to the end because after we see what happens."
Lille were also fortunate not to have surrendered all three points during the close stages.
Bastia substitute Florian Raspentino thought he had netted the match-winner after he was on hand to tuck away Djibril Cisse's effort but his goal was controversially ruled out for offside.
Goalkeeper Mickael Landreau, who spent three years with Lille, believed the linesman made the wrong decision after viewing the incident post-game.
"I think there is no offside," said the 34-year-old France international.
"This is quite surprising (the linesman raises his flag) because it really shows that there is a defender in front of Florian Raspentino.
"Given the rank and importance of these three points, it is normal that there is a lot of anger."
