I think kind of the opposite, more in the Pale Blue Dot mindset, that in the immense vastness of the universe, Earth is all we've got, and should be treated with the utmost significance.
I absolutely agree with that sentiment as well. While we, as a species, are relatively inconsequential, Earth is all we've got (for now!) and it's a special, precious, thing indeed.
Important to whom? The universe itself is incapable of assigning 'importance', so saying that something is unimportant to the universe is just as wrong as saying something is important to the universe. Humans are important to humans, and that's what matters. If only I think I'm important, then I am, to me.
http://www.sciencemag.org/cgi/content/abstract/sci;science.1...
Edit - If you are lacking a subscription:
http://arxiv.org/abs/1009.0518