"We've made it tough for ourselves but hopefully, over these next four games, we will get enough points," the 29-year-old said.
"We've got to be confident. We've got a big, strong squad and the players have proved over the last few years that we are very good in this competition, so we will still have the confidence.
"We know it will be difficult but it's up to us now to show the character and the quality to go through."
Marseille now top the group with six points, leaving Liverpool with work to do to reach the knockout stages again.
They travel to Besiktas for their next fixture in three weeks with another tricky away trip to Marseille looming in their final game.
"If it goes down to the last game in Marseille, it won't be easy for Marseille either," Carragher said defiantly.
"Marseille played very well and I think they deserved to win. Right from the start, we didn't really perform.
"It's difficult to put your finger on what went wrong. We've not played as well as we can in recent games, although we have managed to sneak some results, but this time it has gone the other way."