"Shoegaze" means to look down at your own feet; nothing to do with shoe-shopping. There's actually a style of rock called "shoegaze" (ie. the musicians all seem to be staring at their feet as they play, and not looking at the audience).
Petulance is the irritated way people behave in reaction to small things. A petulant person is annoyed by the smallest of problems.
So... think of a child who's got herself into trouble. The parent is giving the child a talk, but the child is not looking at the parent. Instead, the child is looking down at her shoes. She thinks it's unfair to get such a lecture. She's frowning and pouting. That's your image for "shoe-gazing petulance". :)