Ronald Koeman's side were under pressure from the start and watched as Athletic's Inaki Williams tormented their backline even before veteran defender Gerard Pique was forced off with an apparent injury in the 31st minute.
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"I've not spoken with Pique. I think it's more or less what he had in the week (calf). I don't think it's serious," Koeman said after the match.
Williams fired a sweetly-hit volley from distance shortly before half-time, but the shot went right at Barca keeper Neto and the teams went into the break with the game still goalless.
Eric Garcia, who was ultimately sent off for a clear path foul late in the game, continued to struggle against Williams and the hosts went deservedly ahead soon after the restart from a corner when Inigo Martinez rose up and headed past Neto to make it 1-0.
"It's true that we learned before the game about [Garcia's] grandad dying. He's a great professional and despite that he wanted to play. It's a shame about losing the ball and (the sending off) in the last minute. I think it's a second yellow, but we're happy with him and wish him the best in his personal situation
However, Barca drew level as the half wore on when substitute Sergi Roberto set up Memphis and the Netherlands international smashed a rising volley into the back of the net to set up a tense closing quarter of an hour.
Despite the better second half from Barca, the teams were forced to settle for a point as Koeman's team continued to adjust to life without their former talisman Lionel Messi after he left for Paris Saint-Germain as a free agent this summer.
Of Messi's departure, Koeman said: "I don't always like to talk about the same things, but we're talking about the best player in the world. The opposition have more fear if Messi's playing. It's also [important] for us because if you give Leo the ball, he doesn't lose it. You notice he's not there, but we can't change that."