Are these OK?
They play very well.
If I say;
Whoever loses will be a pity. / Whoever loses will be a shame. (two player)
Whichever team loses will be a pity. / Whichever team loses will be a shame. (two teams)

Question

Are these OK?
They play very well.
If I say;
Whoever loses will be a pity. / Whoever loses will be a shame. (two player)
Whichever team loses will be a pity. /  Whichever team loses will be a shame. (two teams)

Answer

They are grammatically wrong.
Whichever team loses - it will be a pity.
More natural and better would be
It’s a pity that one of these teams has to lose.
It’s a shame that both teams can’t win - they are both playing so well.