My feeling is the squad being gash and the injury hit DCL are the reasons why they won't get rid of him until at least the end of the season. It's unlikely anyone coming in now is going to get a tune out of them any more than he does, although the football is dire from the little I've seen of them.
I didn't watch the game today, but what I got from most Everton fans was that they were expecting to lose, but it was the manner of the loss and how Everton played that would decide whether Rafa should go or not. If it was typically cautious, dull, defensive football from Rafa and still getting spanked they would defo turn on him. Not sure if that's how it went, but if they played it like a derby game then the loss won't be the nail in his coffin.