I don't think it's necessarily always detrimental to the team. If last night's draw knocked England out, then booing would be much more appropriate. It's a way of saying things need to fundamentally change.
With a crucial game still to play, and a side so clearly heavily frustrated and lacking confidence, booing at the end is absolutely never going to improve the team's performance. So either you're an idiot for thinking it will, or you want your team to play badly in the next match.