Lisandro Lopez's injury-time equaliser to cancel out Ryan Babel's 83rd minute screamer means progression into the last 16 of the Champions League is out of their hands.
The Reds must win their final two Group E matches, first at Debrecen before an Anfield showdown with second-placed Fiorentina, to stand any chance of a place in the knock-out stages.
But even then it could count for nothing should the Italians manage to beat Lyon in their own backyard later this month, yet Carragher has refused to concede the Merseysiders face an impossible task.
Belief"We still believe we will get through," said the veteran defender, who was forced to play at right-back in France after injuries ravaged the Premier League outfit's back-line.
"We know it's going to be difficult but we're not out of it yet. All we can do is win our next two games and see what happens.
"We have been in difficult positions before and we've come through like in 2005 and when we had to win in Marseille in the group stages and we came through. It's disappointing but a draw doesn't mean we're totally out of it."
Meanwhile, Carragher was quick to leap to the defence of besieged boss Rafa Benitez who is certain to come under more pressure following another setback for his inconsistent side.
Carragher added: "If you look at the manager's record in Europe we've won it and been to the final and semi-final and quarter-finals. So our Champions League record under the manager has been superb."