The 2010 champion was rocked when it was announced manager Julen Lopetegui would join Real Madrid after the finals.
Unwilling to let Lopetegui stay on for the tournament, the Royal Spanish Football Federation sacked the 51 year-old and placed former captain Fernando Hierro in temporary charge.
Pique, a world and European champion with Spain, is taking inspiration from Michigan's title 29 years ago, when the Wolverines sacked Bill Frieder - who had announced he would take up another coaching position after the Finals - before his replacement Steve Fisher guided the team to glory.
"University of Michigan. Basketball. 1989. NCAA Champion. It wouldn't be the first time it happened," Pique posted on Twitter.
"All together, now more than ever."
Spain begins its campaign with a tough Group B test against Portugal, before clashes with Iran and Morocco.