The La Liga giants moved into the UEFA Champions League quarter-finals with a 2-1 victory over City on Wednesday completing a 4-1 aggregate win.
But Barca's form has been far from convincing, with two losses in their past three league games leaving them four points behind leaders Real Madrid.
Many have written Barcelona off with Bayern Munich in such good form in Europe, but Martino said their efforts against City should hold them in good stead.
"Under any circumstances we need to be very confident from now on after going through to the quarter-finals against such a difficult opponent," Martino said.
"It's not only the fact we went through but how we did it. So we are strong and confident although sadly we need this to transfer into La Liga now."
Martino was proud his side managed to progress despite their recent form, as Lionel Messi and Dani Alves scored either side of Vincent Kompany's 89th-minute goal.
"Obviously in a team such as Barcelona we must always expect this kind of commitment - commitment to the game, to the situation, and to overcome the rival's style of play," he said.
"This sort of commitment is really satisfying.
"Everything we expected from our players they did; possession football, good passing - that's all normal.
"But we understood we are in a difficult moment so it was vital that we went through, especially given the quality of our rival."
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