Alexander-Arnold played a full 90 in last night's Champions League quarterfinal first-leg defeat to Bayern Munich.
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Keane was a long-time critic of Alexander-Arnold when he was with Liverpool.
And he said after Tuesday's clash: "Listen... I'm fed up. The same story in every important match. People keep talking about how well the ball is passed, but what about the basics?
"Defending. At this level, in the Champions League, you can't just switch off like that. It's a childish mistake. Letting Luis Díaz get past you like you're not even there? Please.
"Keep defending like he's never played right-back in his life. Important matches demand great defenders, and right now, he's far from being one."