Bayern took control of their quarterfinal tie with a 2-1 first-leg win in Madrid.
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Real star Vinicius Junior drew criticism from several local pundits for his play-acting over the game.
But Kompany said afterwards: "Vini must continue to be himself. He has my full support, even if he's an opponent.
"Sometimes you need profiles like that. We've had them too, like Franck Ribéry, and we've always appreciated them."
The Belgian added: "Everyone is entitled to their own opinion, but without going too far. I respect Vinicius, regardless of the result."
