The contest at Bilbao's impressive new San Mames stadium was evenly-matched, with both sides creating plenty of chances and the home side perhaps narrowly having the upper hand.
Bilbao goalkeeper Gorka Iraizoz was nonetheless voted man of the match after the 33-year-old denied Darijo Srna in the first half and Douglas Costa in the second to help secure a point for the Basque side.
"A draw was a fair result," Bilbao midfielder Mikel Rico said on UEFA.com.
"We struggled a bit in the second half and we were unable to get on the end of crosses but a point is positive," he added.
"Shakhtar are very quick in attack, they are like bullets. We all wanted to win, but Shakhtar are a great team. They have been playing this way for 15 years."
Shakhtar midfielder Taras Stepanenko said his team had "controlled the game in the first half and most of the second".
"We got one point and didn't concede which is the most important," he told UEFA.com.
"We analysed them. The coach told us how they would play in attack and we were able to shut them out."
Bilbao finished fourth in La Liga last season and are making only their second appearance in the Champions League group stage and their first since the 1998-99 campaign.
The club, coached by their former striker Ernesto Valverde, manage to compete at the highest level even though they only use players of Basque origin.
Group H also includes Porto and BATE Borisov and the Portuguese side got their campaign off to a spectacular start when they thrashed the Belarussians 6-0 on Wednesday.
(Writing by Iain Rogers, editing by Martyn Herman)
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