The hosts raced into an early 2-0 lead at the Coliseum Alfonso Pere courtesy of goals from Sergio Escudero and Lisandro Lopez, but winger Pedro struck three times in eight first-half minutes to put Barca in the driving seat.
Cesc Fabregas went on to add two more after the interval as Barcelona eased to a victory that looked unlikely when they went two down.
Martino was delighted with the impact made by Spain international Pedro, but also lamented his side's slow start.
"(Gerard) Pique should have scored (to make it) 1-0, then we had 10 to 20 extremely poor minutes which could have cost us, but we kept our style and had 70 more good minutes," he said.
"(Pedro) played a fantastic game, he always scores. But it was above all a solid team performance.
"Pedro's secret is that he never gives up. That's why every coach ends us loving him."
Barca were without Neymar and Lionel Messi due to suspension and injury respectively.
While the defending champions go into the winter break top on goal difference, Martino feels his side can find another gear with the return of Messi as well as Victor Valdes and Xavi.
"Hopefully, God willing, Messi, Valdes and Xavi will all be back when we start again in January," he said.
"The team gets better each game. Things we should improve? Keeping clean sheets and defending set pieces better, for sure."
