Four-time World Player of the Year Lionel Messi struck from the penalty spot with 54 minutes gone after being brought down by Martin Demichelis, who was sent off at the Etihad Stadium.
City had their chances but Barcelona dominated possession throughout and were rewarded when Dani Alves struck the second in the last minute to seal a 2-0 win.
Argentinian coach Martino was delighted with Barca's "solid performance" but warned that the tie was not over as they looked to book their spot in the quarter-finals.
He told his club's official website fcbarcelona.com: "I don't have the assurance that we're in the next round, but I do have the tranquillity of doing a good job away from home.
"We came here to win. There was no moment when we thought of any other result that wasn't winning. I think the result is fair.
"I'm focusing on the solid performance from the team.
"We played a bit differently than we usually do when we have three strikers. The selection of an additional midfielder was made in order to have more possession."
The two clubs meet again in three weeks' time at the Nou Camp and Martino added: "We won the first 90 minutes in a match that lasts 180.
"We're going to approach the second leg as if it were 0-0."
Referring to City's progress in the group stages, where the Premier League side suffered a 3-1 home defeat to Bayern Munich before going on to win the away clash 3-2, Martino warned that a comeback is not unheard of.
He said: "City have only lost at home to Bayern and later, in Germany, they managed to win."