Besiktas were beaten 2-0 away to Malmo in Group I on Thursday, with Karius at fault for the opening goal.
A cross from the right wing took a deflection that deceived Karius, who attempted to tip the ball over his own crossbar.
But the goalkeeper only managed to flap at the ball, which landed in his own net, with the goal credited as an own goal by Caner Erkin.
That's not what Loris Karius needed 🙈
The Besiktas keeper misjudges a cross and the ball loops into his front post... pic.twitter.com/ytKvEx67lt — Football on BT Sport (@btsportfootball) October 4, 2018
Erkin was booked for fouling Andreas Vindheim in the penalty box, with Markus Rosenberg stepping up to convert from 12 yards.
Group I is wide open after two rounds of fixtures, with all four teams having taken three points.
Karius kept his first clean sheet for Besiktas at the weekend as Senol Gunes' side beat Kayserispor 2-0 at home.