The 51-year-old saw his side surrender their league title to Atletico Madrid after the two sides played out a 1-1 draw at Camp Nou on Saturday.
Needing a victory to make it five league wins in six years, Barcelona saw Alexis Sanchez's first-half opener cancelled out by Atletico defender Diego Godin four minutes into the second period.
Barca's failure to retain their title means they end the season without a major trophy for the first time since 2007-08, a campaign that was followed by the dismissal of Frank Rijkaard.
Speculation was rife about Martino's future in the closing weeks of the season and the coach put an end to that on Saturday, announcing he would step away from coaching duties.
"I deeply regret not having achieved the goals that this club has always been set and achieved," Martino said.
Martino was appointed Barcelona manager in July, replacing Tito Vilanova, who resigned to fight an ultimately unsuccessful battle with throat cancer.
Luis Enrique, who announced his impending departure from Celta Vigo on Friday, is thought to be the leading candidate for the role.
