The Toffees were beaten 2-1 away at Burnley on Saturday and have won only once away from home in the Premier League this season.
"The finger of blame has to be pointed at that dressing room and the players in there because that's under four different managers," Carragher told Sky Sports.
"We'll chat about Sam Allardyce shortly but that dressing room... the quality in it is nowhere near good enough.
"But also I don't have to watch any of Everton's away games. I just look at a record like that and straight away you know they must be and they are physically and mentally weak.
"That's the only reason you can explain a record like that and that didn't change with what we saw at the weekend."
"Williams getting himself sent off... I think he wanted to get himself sent off. At no time in that game did I feel Burnley were going to lose the game."