The Whites defender featured in the midweek victory over Brentford after being doubtful for the Bees clash but missed the showdown with the Potters after aggravating an ankle issue.
Bielsa opted to rest his club captain for the trip to Staffordshire with Gaetano Berardi stepping into the heart of defence as his replacement.
Cooper is expected to miss Tuesday night's fixture with Nathan Jones' side in the League Cup at Elland Road but should be available for next weekend's Championship clash with Swansea City.
"He could have played today, but he wasn’t at 100 per cent.," Bielsa revealed afterwards.
Berardi stepped in during Cooper's absence as he was handed his his first league start of the campaign.
The 31-year-old forged a strong partnership with loanee Ben White and helped earn United a third clean sheet in a row in all competitions.
Bielsa was quizzed over his defensive options following the game, but admitted he had been impressed by what he had seen so far five games in.
"We have a long season to play," he added.
"The centre-backs in our team are making a very good performance, they are playing very well. But with the passing of the year we will see if the squad that we created has enough or does not have enough (defenders)."
Asked about the convincing victory over Stoke, Bielsa said: "The start of the game was a little bit complicated for us.
"But after we started to manage the goal, then we defended well and we attacked well. Then we had a good performance today and were deserved winners."