The defender reacted badly to the FA’s report on their guilty verdict given to John Terry, and vented his frustrations on his Twitter account.
After the FA claimed his testament was unreliable, Cole labelled the governing body a "bunch of t****", but his Italian boss has denied claims that squad behaviour is poor despite the outburst.
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The Blues manager has also shown his support for his captain Terry, who was banned for four games and fined £220,000 by the FA disciplinary panel for racially abusing Anton Ferdinand, insisting the 31-year-old will continue to lead the side.
He added: "At the moment, he's our captain."