While the Catalans started Wednesday's second leg of their Copa del Rey quarter-final already 4-1 ahead, Levante drew closer in the ninth minute at the Camp Nou when Barcelona midfielder Sergi Roberto put the ball in his own net.
That was as bad as it got for the home side, however, with an Alexis Sanchez brace helping Barcelona on their way to a 9-2 aggregate victory.
Martino said after the game that it was understandable his players had not started at a high intensity.
"I always think that when ties that are played over two games are all but over from the first game, you take your foot off the gas," the 51-year-old Argentine said.
"I was worried in the first 15 minutes because we weren't as intense as we should have been but then we were able to create some good chances.
"I'm happy with how the night went. It went how I hoped it would."
The lead-up to the match against Levante had involved discussion over Martino's future at Barcelona with the club's president Josep Maria Bartomeu saying he wanted to offer the Argentine a one-year extension.
Martino's current deal expires at the end of next season but the former Newell's Old Boys boss said he had yet to discuss extending his tenure with Barcelona and is not in any hurry.
"No, the president has not spoken to me about renewing. That's not true," Martino said.
"I'm very happy with the support I have received from everyone and at this stage I don't need any gesture of goodwill.
"I feel backed by the club, they are content with my work and we haven't spoken about it."
