Martino was left less than impressed after experiencing defeat for the first time as Barca boss in a 2-1 reverse away to Ajax in midweek.
And the Argentine's undefeated domestic record was also ended when Iker Muniain slotted home the only goal of the game 20 minutes from time at San Mames.
Defeat means Barca now lead La Liga only on goal difference from Atletico Madrid, with Real Madrid just three points behind.
However, Martino was much more encouraged by his side's overall display in the Basque country than in Amsterdam five days previously.
"For the first 70 minutes I saw a very good Barcelona side, one completely different from the one the other night. For me, our first-half was one of the best this season.
"Obviously, if we had been able to score first the game would have been very different. The Athletic keeper didn't have much to do, but we had enough chances to score a goal."
With Lionel Messi once again missing due to a hamstring injury, all eyes were on Neymar to compensate for the Argentine's absence.
And the Brazilian had the visitors' best opportunities in either half as he was denied by a fine flying save from Gorka Iraizoz before the break, and then skewed well over when clean through just after the restart.
However, Barca were left enraged when referee Juan Martinez Manuera showed Ander Iturraspe only a yellow card for pulling back Neymar as the Brazilian bore down on goal with the score still at 0-0.
"From the moment Athletic scored it was a completely different match, but we had moments where we controlled the game," added Martino.
"We lacked a little bit of penetration in the final pass, which is something this team normally doesn't have any problem with.
"Moreover, I think there was a very big moment at the beginning of the second-half which could have completely changed the game."
Having gone behind, Martino surprised most by withdrawing both Xavi and Andres Iniesta in the final stages.
But Iniesta insisted he understood his coach's decision to introduce an extra forward in Pedro Rodriguez six minutes from time.
"The coach is the one that acts in the best interests of the team in every situation. There is nothing more to say, he has to think about every player and makes his decisions accordingly."
And despite losing two consecutive games for the first time since April 2012, the Spanish international said the Catalans had to remain calm having previously been on a 20-game unbeaten run.
"Obviously no one likes to lose but we don't need to relate one defeat with the other because they were very different games," added Iniesta.
"We were very good in many phases of the game but we just didn't have the efficiency we needed in front of goal.
"With the demands that we have it is normal that there will be opinions and doubts when we lose, but the most important thing in both victory and defeat is to remain calm and balanced."