Will this really disrupt Spain's on-field play? I imagine they simply insert a top assistant and keep the same structure and tactics. Off-field may be another issue though...?
Apparently they'll have Hierro take over and Celades (U-21 coach) to help him (originally it was apparently planned for Celades to take over, but I think he would've been destroyed by the players.
It might not be that bad, but.... In short, yes, a manager means a LOT... Not just the tactical approach, players have to buy into the system, be willing to sit on the bench, he needs to have good instincts for subs and in-game changes.
Not to mention apparently both Ramos and Iniesta asked for Lopetegui to stay and were ignored.
It's tournament play. You need happy, motivated players, an adequate system (rarely ever anything too elaborate, simply not enough time to develop one), timely subs and changes, luck etc.
If anything, a manager with proper instincts can win you a tournament more often than they'll win you a league.