Babel has accepted the charge for posting comments and a doctored picture of Howard Webb wearing a Manchester United shirt after last Sunday's controversial FA Cup defeat at Old Trafford.
"Ryan has to be responsible. If you are going to be on Twitter you have to be responsible," said the Reds boss.
"You know the repercussions if you say or do something which is contentious.
"He never drew it (the picture) up, he just forwarded it on.
"I think it was a bit tongue-in-cheek, it wasn't his creation and he has apologised unreservedly to the referee.
"The club will take some action I would have thought and then that should be it for me."