On Tuesday, Gordon Taylor, head of the Professional Footballers' Association, said the FA had been "too precious" in its reaction to Babel's tweet. "Where's our sense of humour gone in our game? He's apologised, let's move on," added Taylor.
In addition to posting a link to the doctored picture of Webb, Babel wrote: "And they call him one of the best referees. That's a joke." He subsequently removed the link and wrote an apology on Twitter.
The Dutchman has more than 166,000 other Twitter users following his updates and his messages - and the offending image was subsequently reproduced by some media outlets.
Ryan Giggs scored the game's only goal from a penalty awarded by Webb for Daniel Agger's challenge on Dimitar Berbatov inside the first minute. Webb later sent off Steven Gerrard after 32 minutes for a challenge on Michael Carrick.
Liverpool manager Kenny Dalglish labelled the penalty decision
and also disagreed with the red card for his captain.
Babel later wrote on Twitter: "My apology if they take my posted picture seriously. This is just an emotional reaction after losing an important game. Sorry Howard Webb."
He then joked about spending a spell in "Twitter jail" and his previously prolific posts stopped on Sunday evening.
It is not the first time that a Liverpool member of staff has been drawn into controversy through their use of the website.
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