The Owls suffered a miserable 3-0 loss to the Black Cats on Friday night, further dampening the mood on the blue side of Sheffield as their wait for a first league win of the season continues.
Tony Mowbray's youthful side were in fine form on the night, going 3-0 up after half an hour thanks to goals from Jack Clarke and Daniel Ballard.
But fans were left disgusted after the win after an image of two supporters in the home end at Hillsborough went viral.
The photo shows two men, smiling and pointing an image of the late Bradley Lowery on their phone towards the away end.
Lowery, who was a lifelong Sunderland fan, passed away in 2017 with neuroblastoma at the age of six.
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"We are aware of the images circulating and have launched an immediate investigation together with South Yorkshire Police," Wednesday wrote on X on Saturday.
It continued: "We roundly condemn this outrageous and utterly deplorable behaviour.
"We can only apologise for the undoubted distress caused to Bradley's family and friends."
A section of Wednesday's fans have also started a Go Fund Me page to support the Bradley Lowery Foundation.
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At the time of writing, £615 has been raised.
Lowery touched many people's lives beyond the Stadium of Light during his battle.
He was the club's mascot and also became "best mates" with his hero, then-Sunderland striker Jermain Defo.