A Jordi Alba own goal after only two minutes ensured Barca made a losing start to 2015 and missed the chance to go top of the table.
Real Madrid's 2-1 defeat at Valencia earlier in the day opened the door for the Catalan giants to take over at the summit, but they slumped to a surprise defeat in San Sebastian.
Midfielder Xavi rued a lack of clinical finishing from Barca, but was encouraged by the performance.
He said: "It's a missed opportunity. The ball just didn't want to go in. We had all the chances and missed some very big ones.
"We started off on the wrong foot; the own goal was a killer. But we did play well despite the loss."
Fellow midfielder Andres Iniesta also refused to be downbeat following Barca's third defeat of the season in La Liga.
He said: "We had a shot to get closer to Real Madrid and it's a shame because the own goal was early and we had time to turn things around. We controlled the match for the most part.
"The only thing we didn't do was score. The team played well, good rhythm, we passed well, we just couldn't finish.
"In past years the long balls really hurt us, but it could have been worse today.
"We want to play well this month because we have a lot of games. We play every third or fourth day so we have to look at our pluses and fix our minuses."
