The midfielder was at fault for the Italians' equaliser, as his misplaced pass allowed Fabio Quagliarella in to deny the Blues all three points in their opening Champions League Group E game.
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Chelsea wrote on Twitter: "Abuse on social networks is abhorrent. Racist tweets towards Mikel are totally unacceptable. Police informed. #CFC supports strongest action."
Two hours earlier, the Stamford Bridge side had tweeted to deny reports that the 25-year-old had been targeted through the site but have now been forced to backtrack.
The original tweet read: "Not true Mikel quit Twitter due to messages received. He'd wanted to leave for a while & deleted his acct today without looking at it. #CFC"
Mikel accepted full responsibility for his mistake after Wednesday's game, telling Sky Sports: "I'm disappointed, it was my pass and I over-hit it."