Spanish media have reported unrest in the dressing room lately, with Martino feeling the pressure after being dumped out of the Champions League and slipping down to third place in the La Liga standings after a shock 1-0 defeat to Granada over the weekend.
Yet Puyol insists Martino still has the respect of the squad, who are looking to finish off the season on a high.
“We are behind Tata all the way,” the Spanish centre-back told the club’s official website.
"I don't think there needs to be a revolution depending on the results.
"You have to have a working method, not just according to whether you win one or two trophies.
"The team is hungry, it wants to win and keep making history."
Barca are still in with a shot at League glory and are in with a good chance of adding to their trophy cabinet when they face arch rivals Real Madrid in the Copa del Rey final on Wednesday evening.
"We have a final ahead of us - one of the best possible games - and I want to assure the fans that we will be giving everything in the game," Puyol stated.
"If we are all united then it will be easier. The only way forward is to stay together."