Iker Muniain's 70th-minute goal inflicted Barca's second consecutive loss in all competitions, but Martino's men remain top of La Liga on goal difference.
Martino felt his side did enough to deserve something out of Sunday's encounter, even labelling their first-half display one of their finest of the campaign.
"If I had to speak about the first 70 minutes I would say Barcelona are (doing) well. I think the first half from my team was one of the best performances at La Liga this season," he said.
"We did enough even to take the advantage and if we had done that the match would have been different.
"We made enough situations to get something from this match."
Without the injured Lionel Messi, Martino lamented his team's struggles to play the final pass in the attacking third.
"I think to the 70th minute, when Athletic scored, we were better. Not only in the first half even in the first 20 minutes during the second," Martino said.
"I think after Athletic's goal the match changed but we had so many good moments with the possession of the ball.
"We didn't make the last pass and this is strange for this team."
Martino had demanded a response from Barcelona after their surprise 2-1 loss to Ajax in the UEFA Champions League on Tuesday.
It was the first time since March that Barca have suffered consecutive losses and Martino was disappointed by the back-to-back defeats.
"Obviously because this side are not used to this kind of situation (losing matches)," he said.
"Barcelona are not used to losing two matches in a row and we came here to try to sort the match in Amsterdam out.
"For that I think it is a shame we didn't get any point when my players deserved more to take something to Barcelona."
