Martino replaces Alejandro Sabella in the role - and the successor said he would aim to continue the foundation of work in place from his predecessor, who led the Argentinians to the final in Brazil, where they lost in extra-time to Germany.
But Martino said he still felt the pain of his failures at Barca, as he fell short of winning the La Liga crown in his lone season in charge at Camp Nou.
"I'm absolutely dissatisfied with the year that has passed but always thinking that I'm the man responsible," the 51-year-old said.
"For sure, there were justices and injustices. It's hard for me to tell which were the justices and which the injustices.
"But I can tell, as I said when I left Barcelona, I feel responsible for the really bad year of Barcelona."
The bonus, however, of Martino's switch from Barca to Argentina is his chance to work with Lionel Messi and Javier Mascherano again.
Martino said he hopes to build relationships with his key squad members, as he begins his reign in charge of the nation he represented once as a player.
"I think it's very important to have fluent contact with the players that I will coach," the former Paraguay coach said.
"With Leo and Javier, I had contact with them during the year. The faster and deeper I will know the players, the easier my job will be."
He added: "Leo's role, here, in Barcelona or everywhere he would go, is the role of the best player in the world and the responsibility that brings, and sometimes it seems that a lot is not enough if it is not the maximum.
"In the case of Javier, I have the feeling that you've discovered now a leadership that, for me, existed for some time."
