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"The details of how the situation developed I don't know (but) I have no doubt Jorge (Messi's father) and Lionel had some influence," Martino, the former Paraguay coach, told a news conference in Rosario.
"I'm sure they were asked their opinion and we've come to this outcome," added the 50-year-old, who comes from Rosario like the Messis.
Martino, who led Newell's Old Boys to the Argentine "Final" championship last month, added: "I was expecting some job proposals and I can't say I was expecting this one.
"The situation was unexpected and of course it took me by surprise," added Martino, who quit Newell's after they lost their Libertadores Cup semi-final two weeks ago.
Barcelona went in search of a new coach after Tito Vilanova had to step aside to undergo more treatment for throat cancer.
"This is a very important job opportunity which came about due to a very unfortunate occurrence (Vilanova's illness)," Martino said.
"I'm very grateful they considered me, my staff and my work. The quality of the Barcelona squad, with Lio, is something any coach desires.
"I'm sure in our day-to-day (work) we'll find ways to support (Messi) so he continues to be the extraordinary player he is."
Martino, who will travel to Barcelona on Thursday, said he hoped to be up to the high demands of coaching one of the world's best club sides.
"We'll try to fit in quickly... Barcelona is an institution that has a way of life, a footballing development. We are the ones who are going to step into that world."
One of Martino's staff is Adrian Coria, the man credited with discovering and coaching Messi from the age of 11 to 13 at Newell's.
Martino misses Barcelona's friendly on Wednesday against European champions Bayern Munich, now under the Spanish giants' former coach Pep Guardiola.
Saturday's friendly with Norway's Valerenga in Oslo could be his debut on the bench. (Additional reporting by Luis Ampuero in Buenos Aires; Writing by Rex Gowar in London, editing by Pritha Sarkar)
