Warnock sprang to Suarez's defence, despite seeing him score the only goal in Liverpool's 1-0 victory at Anfield on Saturday.
Suarez was charged with improper conduct by the FA after allegedly making an obscene gesture to Fulham supporters at Craven Cottage last week.
And he is already the subject of an FA charge over claims he racially abused Manchester United's French defender Patrice Evra. But Warnock believes it is those clubs whose fans make a point of goading Suarez who should also find themselves in the dock.
"It is easy to criticise," said Warnock. "He is a foreign player in a foreign country and the crowd away from home gives him so much stick.
"He should be protected from that as much as possible.
"Yes, he has to learn he cannot be making gestures, but the stick he gets, it is about time someone did something about it.
"They are so quick to charge him in terms of him putting a finger up. Look at the abuse he is getting and charge the clubs concerned. If the supporters are going to give abuse like that, then the stewards (in the crowd) must hear it. But they turn a deaf ear."