Martinez scored an early opener for Antonio Conte’s team, Inter’s first goal at the Camp Nou since 1970, to raise hopes of a memorable victory.
However, a double from Luis Suarez, including an 84th-minute winner, condemned the Nerazzurri to their first defeat of the season in all competitions.
The defeat means Inter have now lost three consecutive away matches in the Champions League for the first time. It also leaves the Serie A outfit bottom of Group F with one point from their opening two matches.
Conte, who was warned by the officials about his conduct, criticised the referee after the game and said he should have shown more ”respect” towards the Inter players.
The former Chelsea boss was left frustrated when the referee failed to award a penalty for what he thought was a foul on Stefano Sensi.
He did, though, praise his side’s display, labelling it a “great performance” and insisting they did not deserve to lose.
Martinez agreed with his coach and believes the team need to take encouragement despite the disappointment of the final result.
“The coach is right. We produced a great display and didn't win because of fine margins,” Martinez told Inter’s official website.
“Now we have to think about Juventus. We leave here disappointed because we deserved to win.
“We have to be alert in this competition because players of this calibre are unforgiving if you make a mistake.
“With all the good work that we did, we didn't deserve to lose. The referee also played a role, but we have to be more focused.
“I do think we produced a very good performance and we can be pleased with that albeit disappointed with the result.”
Inter’s European frustrations are in contrast to their domestic form, where they sit two points clear at the top of Serie A with six wins from their opening six matches, scoring 13 goals and conceding just two.
Next up for Conte’s side is a huge encounter with second-placed Juventus, champions of Italy for the past eight seasons, at San Siro on Sunday.