Babel fined over Twitter outburst
Webb, who officiated at the World Cup final last July, awarded United a penalty in the opening minute which Ryan Giggs converted to give the home side a 1-0 win at Old Trafford.
"Social network sites, like Twitter, must be regarded as being in the public domain," the English Football Association's (FA) Roger Burden said in a statement on Monday.
"All participants need to be aware, in the same way as if making a public statement in other forms of media, that any comments would be transmitted to a wider audience. It is their responsibility to ensure only appropriate comments are used," Burden added on the FA website.
Babel posted a mocked-up picture of Webb wearing a Manchester United shirt.
"And they call him one of the best referees? That's a joke," wrote the Dutch international, who did not play in the World Cup final that the Netherlands lost 1-0 to Spain, on the social network.
Babel later apologised and was warned by manager Kenny Dalglish to be more careful.