A Nolan Roux brace secured Lille the three points at Grand Stade Lille Metropole as they inflicted a first league defeat of the season on Claudio Ranieri's side.
The victory was Lille's fourth Ligue 1 success in a row but Girard is keen for his players to remain focused despite their impressive form.
"It's a great win. We wanted to see where we stood in relation to a terrific Monaco side, and we're very happy," he said.
"It was a wonderful night... with our fans pushing us all the way. We had some good fortune both in attack and defence, but I never allow myself to feel that I've been beaten before the match has been played, and I told the lads that.
"You just have to give that bit extra against the big sides, and what the lads pulled off tonight was no accident. Still, we mustn't get carried away, it's just one match.
"But we needed to persuade ourselves that we could be an excellent side. It was great to see the lads enjoy themselves and play good football."
Lille sit second in Ligue 1 and have not conceded in seven top-flight matches, letting in just four goals all season.
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