Athletic lost on just two occasions at San Mames in La Liga last season and enjoyed plenty of the ball in Wednesday's Group H encounter, but their lack of cutting edge in the final third allowed Shakhtar to claim a valuable away point.
Ukrainian champions Shakhtar, who were lively on the break, have won all six of their domestic matches this season and they could have led at half-time had Athletic goalkeeper Gorka Iraizoz not made a well-timed intervention from Darijo Srna's cross to deny Alex Teixeira an easy tap in.
The hosts' best sight of goal in the opening period came from Ibai Gomez, who showed quick thinking from a long-distance free-kick that went just wide.
The match was a frantic end-to-end affair after the break, with Shakhtar's lightning pace on the counter causing Athletic trouble.
Shakhtar's Douglas Costa brought the best out of Iraizoz with around 20 minutes to go, but the game finished goalless.
Athletic settled well and created the first opportunity in the third minute when Oscar de Marcos found space on the right before picking out Mikel Rico in the penalty area, only for the midfielder to fire wide.
Shakhtar too looked dangerous in an open start to the match and Taras Stepanenko tested Iraizoz with a low 20-yard drive from the left.
And Iraizoz was called into action again in the 17th minute.
With Athletic captain Carlos Gurpegui off the pitch following a heavy collision with Marcio Azevedo, Srna provided an excellent low cross into the area, forcing Iraizoz to parry to safety with Teixeira lurking.
Shortly before the half-hour mark, Athletic's Gomez almost caught Shakhtar off guard with an audacious free-kick wide on the right that curled into the side netting.
Athletic then had a penalty shout shortly before half-time when Yaroslav Rakitskiy nudged Aritz Aduriz to ground in the area, but referee Anastasios Sidiropoulos was unmoved.
The hosts' midfield controlled possession at the start of the second half, but the best they could muster on goal was Aymeric Laporte's tame effort that was easily held by Andriy Pyatov.
As the half wore on, Shakhtar looked arguably the more likely to score, Laporte making one particularly crucial block to deny Teixeira.
Iraizoz produced a fine stop from the lively Douglas Costa in the 68th minute, cutting onto to his left-foot before fizzing a 20-yard shot that the keeper turned away low to his right.
Shakhtar did have the ball in the net soon after when Oleksandr Kucher's header was tapped home by Teixeira, but the whistle had long since gone for offside.
The visitors appeared to tire as the match neared a conclusion and Athletic dominated the final 15 minutes.
Again, though, Ernesto Valverde's side were left wanting in the final third, as Markel Susaeta came closest by stinging the palms of Pyatov from the edge of the box in injury-time.
