Stage 1: Participants/Teams are given a task in which they have to excel.
Stage 2 : They then realize that they are an important part of the big picture
We give them small pictures which they have to replicate on a bigger scale. Once they are done, these pictures are stuck together in a giant collage. Realization dawns that they are a part of the big picture and unless their contribution is perfect they do not get the perfect big picture.
Alternatively the debrief would emphasize on the participants looking at the big picture instead of nitpicking.