When you are displeased by something and you let your gloomy mood show, you're sulking. Do you want to bake another cake, or are you going to sulk all day about the one you dropped?
When you say someone sulks, the tone of the word suggests the person is overdoing it. You wouldn't accuse a widow of sulking at her husband's funeral, because she has a good reason to be sad and gloomy. Instead of sulking because you messed up your tuba solo during the concert, why not put your energy into practice? Or switch to violin.