Having already accepted a charge of improper conduct, Babel was also warned about his future conduct.
The Netherlands international posted a digitally altered picture of referee Howard Webb wearing a Manchester United shirt after being angered by the decisions in Liverpool's 1-0 loss at Old Trafford in the FA Cup last weekend.
Roger Burden, the chairman of the FA's regulatory commission, says that "social network sites, like Twitter, must be regarded as being in the public domain."
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