The Spanish side progressed to the quarter-finals as they defeated Manuel Pellegrini's men 2-1 in Camp Nou on Wednesday, winning 4-1 on aggregate.
The Barca coach said his team came up against a formidable opponent in their second round tie and feels the fact that they emerged victorious in both legs shows that they can beat any side in the competition.
"We won 4-1 with two wins against a very good opponent collectively and individually," he told reporters after the game.
"When we play like that we can beat any opponent.
"Tonight we faced the best rivals we could have been drawn against and a team who could have gone further in the tournament. The game was one that needed to be overcome."
The 51-year-old then praised City and admitted they struggled to deal with them at times.
"There were moments in which we had control and others in which we struggled. City played more of the game 11 against 11 and they were more dangerous then.
"It was predictable that City would have the ball at certain points. We didn't feel at ease when not in possession and we struggled at dead-ball situations.
"Manchester City are not a team you want to be sharing possession with and that's why we played the way we did tonight. It's probable that we will [continue] to play that way when we come up against sides who can work the ball around well."
Martino then went on to thank his team's fans for the support they showed throughout the 90 minutes.
"We not only have to single out the presence of our supporters tonight – their attitude and backing of the team [was also impressive]. We really needed that and I think it was an acknowledgement of these players who have given so much to this team."