Defender Carragher - captain in the absence of Steven Gerrard for Saturday's shock FA Cup home defeat by Barnsley - said: "I wouldn't call for and we have to fight this just a bad spell, it has been a lot longer than that."
Admitting Benitez's team are in crisis and that fans' patience is stretched to the limit, Carragher added: "We realise we aren't playing well enough.
"It's not a matter of putting your finger on one reason: it's simply because we haven't been good enough. The sooner we get out of this run the better. We've still got the Champions League to play for that fourth place, so every League game is important. We have to make sure we're in the Champions League next season.
"You get feedback from supporters all the time. Obviously they're not too happy about things. Myself and Stevie, because we're local lads, hear a lot from supporters and we're supporters ourselves.
"We aren't stupid, we know what's being said. The supporters are as disappointed as we are."