Wendersen Galeno proved the matchwinner as Porto won the first-leg of their round 16 tie 1-0.
Arsenal didn't have a single shot on target in Wednesday's match.
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This has not happened since they lost 1-3 to Barcelona in the same tournament in 2011.
Back then, Sergio Busquets was responsible for Arsenal's goal when he sent the ball into his own net by mistake.
Arsenal have now lost their last five matches in the knockout phase of the Champions League.