Harry Redknapp's job this season, I believe, was to get us Champions League football. Of course, I have no evidence for this, but given what we know Levy has said in the past, etc etc, that was Redknapp's goal. He failed. Thus, should go. If a managers job was to 'avoid relegation' and they finish 18th, on goal difference, they still got relegated, and would probably get sacked. This is no different.
We didn't get CL. Forget 4th, or 3rd, or 9th, or 18th. Champions League. Are we in it? No.
Redknapp failed, it really is that simple.
As for who to replace him?
I'll champion Louis Van Gaal's corner. I know it won't happen, but I can dream.