The player losing graciously is still allowed to care about losing.

Good manners in defeat are not the same as indifference. Shaking hands and meaning it does not require pretending the result did not matter, and pushing people to perform lightness takes something real away from them. Caring is why the game was worth playing at all. Grace is a description of how you behave rather than of how much you feel.

After a loss that stings, let yourself be disappointed for a while without apologising for it. When somebody else loses, avoid telling them it does not matter, and say instead that it was close, if it was.