Despite admitting his satisfaction at the draw, the 57-year-old trainer believed his men could have gone for the win had they possessed more conviction
Javi Guerra and Alberto Bueno struck early to put pressure on their Basque visitors, before Oscar de Marcos and Markel Susaeta restored parity at Jose Zorrilla.
"We did well to overturn the 2-0 deficit, but we should have gone on to win the game" Bielsa said to reporters after the match.
"We controlled proceedings, defended well for the most part and looked sharp in attack. We just lacked a certain spark, as well as the tranquillity to finish chances off.
"We deserved to win this game."
After the highs of reaching the Europa League and Copa del Rey finals last season, los Leones have struggled this term and are languishing in 13th place as of Saturday night.