Having looked like clear favourites for the Primera Division title, Barca are now in the thick off a three-way battle with the two Madrid clubs and a 1-1 draw at the Ciutat Esportiva did little to aid their cause.
It was only the fourth time this season they have lost points but, with Atletico and Real alongside them, every slip is vital.
They were not punished fully for this one, with Sevilla holding Atleti to a 1-1 draw straight after, but Martino was still unhappy.
"This (the draw) isn't what we came here for and nor was it what we deserved," he said on his club's official website.
"We were not fortunate in front of goal, (but) the season will bring about many more surprises and the remaining 18 rounds of the season will show that.
"We're leaving sad because we were unable to win. We know that we're going to win nine out of 10 of these types of matches."
Martino's frustrations were shared by Lionel Messi who, along with his team-mates, was denied time and again by the resolute Levante defence.
"It's a shame, we did everything possible to win but they closed off at the back and didn't give us any space," he said.
"It's a difficult stadium to play in, but we tried. We did enough to deserve to win, just lacked a bit of luck."
The sides will meet again in the Copa del Rey on Wednesday.