The 31-year-old has also revealed that he prays to God every night in the hope that the Reds can start to climb the table.
Sunday's 2-1 defeat to Arsenal at Anfield, their sixth Premier League loss this season, left Benitez's side seventh in the table, 13 points adrift of leaders Chelsea and five behind fourth-placed Aston Villa.
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Liverpool have already crashed out of the Champions League at the group stage and will be playing in the Europa League in the new year.
Carragher said: "It is tough at the moment for everyone associated with the club but we've been here before.
"Part of playing for Liverpool is having character and that is what we need at the moment.
"Between now and the end of May it's got to be a grind at times but we've got to stick together, get through it and, as I'm doing every night, pray to God that at the end of the season there will be something worth what we've gone through at times, because it's been tough.
"I pray to God we win the FA Cup or the Europa League and we get in the top four, dust ourselves down at the end of the season and say 'It hasn't been so bad in the end', but at this moment it is tough.
"With the quality of players we have and the stature of the club, we realise we should do better. We can't look for excuses. We have to be big and strong and get on with it."
Source: DSG
