Put it right after the failed moment, before the reaction shot, so the pout becomes the payoff. Follow it with a sad violin to stretch the joke, or lead in with a wrong answer sting when a quiz guess goes badly, then let the pout close the scene.
About this sound
This is a soft Korean vocal whine built around the sound “bbueng,” a drawn-out pout with no words, just a wobbly, childlike cry. It feels cute and deliberately overdone, turning a small disappointment into something silly rather than sad. It comes from Korean online slang for playful sulking, where the noise is used to act upset without meaning it.