Arteta was left unhappy with ref Michael Oliver after Leandro Trossard's first-half dismissal.
But Keane said in his role of pundit: "Managers are coming out every week saying every decision is against them.
"Just come out and accept it.
"Deep down he'll be satisfied with a point. Show a bit of class, manager of Arsenal. He probably deserved the red card, we reacted well and we move on.
"That's the end of it. Take your medicine and move on. Show a bit of class.
"Wouldn't it be good if a manager came out after a game and just said: 'Yeah, you know what he was a bit silly, it was a yellow card'.
"Every manager is coming out every week going: 'No, it wasn't a foul, it wasn't this, something happened five minutes earlier'.
"Just come out and be big enough… players do daft stuff on a football pitch, come out and show a bit of class and say: 'The referee gave him a chance to send him off. We're disappointed but we move on'.''