The pair clashed at the end of the game, with Conceicao wagging his finger at Arteta.
He later said: "The result was unjust. We deserved to go through.
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During the game and towards the bench he, in Spanish, I don't know if this is to do with Spanish managers, he insulted my family.
And then at the end, I said attention, who he insults is not between us, he should focus on training his team because they have a lot of individual qualities to do that."
It's been suggested Arteta strongly denies Conceicao's claims.