The Basque side went 2-1 up in the closing stages of the game after a Gerard Pique own goal, but they were unable to successfully defend their lead as Lionel Messi restored parity in the first minute of stoppage time.
"It is very frustrating not to have beaten Barcelona. It might not have been deserved if we had managed to do so, but we came very close in the end. Either way, the final score is a good reflection of what happened on the pitch," Bielsa said at the post-match press conference.
"It was an even encounter and both teams had to put in an incredible effort to match each other. There were some very interesting battles going on on the pitch, for example the one between [Iker] Muniain and [Eric] Abidal. That duel summarised the game perfectly."
Athletic Bilbao are ninth in the Primera Division table following the weekend's results, while Barcelona sit second, three points behind Real Madrid.
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