Angel Di Maria scored twice last week, with Julian Draxler and Edinson Cavani capping a magnificent performance from Unai Emery's men as Lionel Messi and Co fell well short at the Parc des Princes.
No side has ever overturned a four-goal deficit from the first leg in a Champions League tie, putting Barca's task in sharp context.
A frosty reception welcomed the team back to Camp Nou as they edged out struggling Leganes 2-1 on Sunday, but three-time Champions League winning Barca captain Puyol believes all is not lost in Europe this season.
"This is a time for the team to be united," Puyol told reporters.
"By sticking together, they can get through this situation. We know that the result in Paris hurt, but if there is any team that can turn something like this around, then that team is Barca.
"It is a difficult result, but not impossible. This team has done a lot in recent years and they deserve every confidence in the world.
"I am with them to the death, not just because they are friends of mine but because at Barca we are all in the same boat.
"We cannot afford to have doubts. We have to fight to the end."