The Group H fixture - which was the first professional meeting between the two sides - saw Lionel Messi once more steal the limelight with a superb hat-trick, while centre back Gerard Pique also got himself on the scoresheet.
But the Spanish champions only led 1-0 at the break through Messi's fierce free-kick, and Martino was disappointed with his side's lack of composure to that point.
However, after watching them turn on the style in the second period, he praised their response.
"We were better in the second half and in the passing game," Martino said. "We did not play well in the first half, with many long balls.
"We still made mistakes, but we are improving game by game.
"It is very important for me and for the club to begin with a victory in the UEFA Champions League group stage."
Midfielder Andres Iniesta was delighted to start with a win, but insisted his side have to be more tactically aware.
"It is important to start winning in the competition," he said. "We have tried everything and have been effective in the decisive moments.
"It's a matter of growing up. Each season we must grow with the passage of the matches and we have to find a balance. We have to know when to attack and when to defend."
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