The case stemmed from an incident in Leeds' game against the Addicks at The Valley back in September and was settled last week, with an independent regulatory commission finding an allegation that Casilla racially abused Leko to be proven.
It was alleged that he used the n-word in the direction of the forward, who was on loan to Charlton from West Brom at the time.
Charlton's statement said they were pleased the matter had been brought to a close, but revealed Bonne and Leko have since been targeted on social media.
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A spokesperson said: "The club is pleased there is finally a resolution following the news that Leeds United goalkeeper Kiko Casilla will be banned for an incident that took place when they played at The Valley in September.
"However, the club is disappointed with the abuse on social media that Jonathan Leko and Macauley Bonne have received following the news. Jonathan was a victim in this incident and the pair of them did not ask for this, the club is proud of both of them for standing up as football continues to fight racism.
"Charlton Athletic’s priority in the process has been supporting the players involved. Racist abuse is abhorrent and completely unacceptable, at no point should an individual have to experience racist abuse on the football pitch or in any walk of life."
Charlton say this is not the first time one of their players has been subjected to racist abuse and vow to work with anti-racism campaigns to play a part in eradicating it.
"Last year the club twice reported racist abuse on social media directed towards Lyle Taylor to the police.
"All of us in football still have so much work to do.
"The club will continue its work with various anti-racism organisations and the Charlton Athletic Community Trust on anti-racism and anti-discrimination projects and urges anyone who witnesses racist abuse to report it."