Iniesta played the full 90 minutes in Barca's 3-1 defeat at Real Sociedad on Saturday - a result that means the champions are now second in the table, three points behind Real Madrid.
Even though the Catalans are in the running to retain their league crown, are well placed to reach the quarter-finals of the UEFA Champions League and face Real in the Copa del Rey final in April, speculation is rife that Martino could leave Camp Nou at the end of the season.
But Iniesta has defended the Argentinian and says the team are fully behind him.
"The manager trusts the team to win and he always wants the best for his team, therefore, the players have no doubts regarding the manager. On the contrary, we are with him to death," the Spain international told Barca's official website.
"We played really well in the matches leading up to this weekend, but the defeat to Real Sociedad was tough. The players and the manager are, in the end, responsible for everything.
"Starting now everything is practically a final. We have to win all of our games if we want to reach the end of the season with options to win the title."
Barca's title rivals Real and Atletico Madrid face-off in the league this weekend, but Iniesta has no preference as to who he wants to emerge victorious at the Vicente Calderon.
He added: "You never really know what the best outcome is. We're one game away from being leaders and we have to face both teams.
"It's clear that we depend on ourselves, and we have to do a good job. If we don't do our job it's of no use to us if Madrid or Atletico win this weekend."
