To be ranked worse than F went down badly (6)
I believe the answer is:
grated
'went down badly' is the definition.
(something which grates is received badly)
'to be ranked worse than f' is the wordplay.
I cannot really understand how this works, but
'be' could be 'rate' (rating is a kind of being) and 'rate' is found in the answer.
This explanation may well be incorrect...
(Other definitions for grated that I've seen before include "Shredded (eg, carrots)" , "Made a harsh sound" , "Rubbed harshly as on nerves" , "Nutmeg and cheese often are" , "Shredded; was discordant" .)