Martino's only success in his one year in charge was winning the Spanish Super Cup and Garcia, a former Barca player himself, thinks that his style of football didn't suit the club.
"Maybe it was a bit like a crash between [Martino] and the players, not personally but maybe on the way to play," Garcia told Sports Mole on Saturday at the Heineken Ibiza Final.
Recently-retired Garcia played with Enrique during his career and thinks that his character will suit managing a club of Barca's stature.
"It's not easy to manage Barcelona because you have very big games," he added.
"You're surrounded and it's not easy with the press, the fans and always being in the spotlight, but he's got the personality, he's got the character. As a player, he was a winner."
Enrique has previously managed Barcelona's B team, Roma and Celta Vigo.