The Gunners laboured to a lethargic triumph over the Ukrainian giants at the Emirates, where an unfortunate own goal from Shakhtar goalkeeper Dmytro Riznyk separated the two sides.
Arsenal were not without additional opportunities to extend their lead, but a lack of incisiveness nearly cost them dear, as David Raya was called upon to make some crucial interventions in the latter stage of the match.
Arteta's men once again struggled on the creativity front without the injured Saka and Martin Odegaard, both of whom were pictured watching on in the stands as they recuperate from hamstring and ankle problems respectively.
Arteta was asked about Saka's chances of facing Liverpool in Sunday's crunch Premier League clash, but he is not optimistic of seeing his star winger recover in time, telling Amazon Prime: "I don't know, he wasn't able to train yet so that's unlikely."
Arteta delivers Calafiori latest and reveals reason for Ben White substitution
Saka, Odegaard and Kieran Tierney - out for the long-term with a hamstring injury - have now welcomed another face into the infirmary, as key defender Calafiori was taken off in the second half with an apparent knee problem.
The Italy international suffered an awkward slip as he tried to make a tackle, and he initially tried to play through the pain before being replaced by 18-year-old academy graduate Myles Lewis-Skelly.
Calafiori went straight down the tunnel for further assessment, and Arteta had no positive news to share on his condition either, although he did confirm that fellow defender Ben White was taken off at half time for tactical reasons.
"Ben was my decision to take him out, he had a yellow card, we have played enough with 10-men in certain periods. They had a lot of intensity on that side and a lot of attacking players on this side," Arteta added.
"We didn't want to take any chances. With Riccy it's something different, he felt something, I don't know the extent of that so in that sense it's not great news."
Should we believe Arteta's injury updates?
When it comes to injuries to star names, if the evidence is irrefutable, Arteta will normally call a spade a spade and deliver the news straight. If he does not have to, then he will play mind games with the media.
Flash back to October 2023, when a smiling Arteta repeatedly insisted that Saka would be "in contention" for the visit of Manchester City following an injury, only for the attacker to miss out entirely.
The Spaniard also refused to rule Odegaard out of September's North London derby win over Tottenham Hotspur, even when it was otherwise clear that he would be out for some time, so fans have learned to take his injury updates with a huge pinch of salt.
Ahead of such a mouthwatering game against Liverpool, expect Arteta to either remain cryptic or use his smoke-and-mirrors tactic in his pre-game press conference, and there is still every chance that Saka and Jurrien Timber (muscle) will be fit.
However, there is undoubtedly more concern regarding Calafiori given the awkward nature of his fall, while Odegaard, Tierney and Takehiro Tomiyasu (knee) are all set to miss out alongside the suspended William Saliba.