The Monaco playmaker faces six weeks on the sidelines after straining knee ligaments during the club's UEFA Champions League final defeat to Porto.
The ill-timed injury has scotched his prospects of playing for the holders in next month's European Championship in Portugal.
But, while upset to lose his place in Jacques Santini's squad, Giuly is grateful it is not a long-term knee problem, which he has suffered from in the past.
"It is just a strained muscle and it is not too serious," Giuly told L'Equipe.
"But I was really scared and I could see myself once again going under the surgeon's knife.
"I freaked out.
"With rest and treatment, it will be cured without any trouble. I am already in less pain than during the previous few days.
"It is a disappointment to miss the Euros. It should be my first great competition with the French team and it is so sad to miss it.
"I really wanted to experience that and I worked hard to achieve that. The last week has left me with a bitter taste."
