Martino's future at the Nou Camp seems uncertain after the Catalan giants bowed out of the Champions League with a defeat at Atletico Madrid and then lost 1-0 at Granada to leave their La Liga title chances in tatters.
However, Puyol insists that he and the rest of the Barca squad still have full confidence in the 51-year-old.
"It is easier to criticise the manager than 25 players," Puyol told reporters. "But if things go wrong it is everyone's fault.
"I wish him the best. He's a great coach and has another year of his contract. We'd die for him and him for us."
Barca's most realistic chance of winning silverware this season is by beating Real Madrid in Wednesday's Copa del Rey final.