Docter, a father of two, wrote and directed Pixar's double Oscar-winning film Up, as well as Monsters Inc, and named the young heroine of Up after his daughter Ellie, who also voiced the part.
"My daughter was very like the Ellie of Up - spirited and sparky," he explains. "But then as time went on, she became quieter and more withdrawn. It was really hard to know what she was thinking as she started to grow up."
Producer Jonas Rivera adds: "Inside Out is our attempt to answer Pete's question of 'What's going on inside my daughter's head?'
"We didn't know either. I think a lot of parents ask that question."
Each emotion is given a distinct colour and shape, from the green of Disgust - a homage to Riley's hatred of broccoli - to the red block of Anger, who emits fire when disturbed.
This, according to Poehler, who runs an online community for girls and women called Smart Girls, could be a step forward for children trying to articulate their emotions.
She says that, as the mother of two boys, she knows how hard it is for children to say what they feel. "What [the film] does is give you the tools to talk about emotions and feelings which isn't very easy to do all of the time."
It would be satisfying, she says, to hear a child say, "I feel like Anger today" because he or she can visualise it.
However, Docter denies that Inside Out is Pixar "doing" psychotherapy for children - or for adults, who, he believes, could benefit just as much from the film.
"So many adults employ therapists because they can't express themselves," he points out. "As a kid, at least if you are angry you lie on the floor and kick and scream, but as we grow up we realise it's not socially acceptable to do that and sometimes we bottle things up.