Burley claims the Spaniard's position in west London is now untenable.
"The best scenario for both would be if Rafa Benitez moves on ASAP," he told talkSPORT. "The situation isn't going to get any better.
"Chelsea fans are entitled to their opinions but from day one it's been over the top.
"He's not the only manager who's ever said anything about Chelsea while he's been in charge of another club.
"If you've been at Chelsea recently the atmosphere has not been great and that transfers onto the players.
"He's been taking it full on for weeks, everybody has got a snapping point and he showed his on Wednesday night."