The 33-year-old, who made 51 appearances for Les Bleus, wrote a letter of support for each member of Didier Deschamps’ World Cup squad.
However, a tearful Koscielny explained how part of him wanted France to fail in his absence.
“I will always be a supporter of France because it remains a team that represents our country, but I will not wear the blue jersey.
“I wanted France to progress [at the World Cup] and at the same time I wanted them to lose. It’s selfish, but it’s life. Some people will say, ‘What do you mean, he wanted France to lose?’ But that was my feeling at that moment.
“I think France’s victory did me more psychological damage than my injury.”
“He sent me a text for my birthday in September, otherwise I did not have contact with him,” said the centre-back.
“It feels like being hit around the back of the head.”
A return to training is pencilled in for November, and Koscielny hopes to be able to fight to regain his place at Arsenal, where he is contracted until 2020.