"We haven't been able to maintain our hunger and the conviction we needed to make a serious attempt at defending the trophy," said Alonso. "That's the saddest thing."
"Mentally, we were not fully prepared for this World Cup and physically, we were right at the very limit. Both of those things together meant that we weren't in better conditions. We weren't at the required level and we deserve to have been knocked out."
Spain lost their first match to the Netherlands 5-1, and was ousted from the World Cup on Wednesday when Chile defeated them 2-0.
Spain's coach Vincente Del Bosque finds his position in question after the team's early elimination and Alonso urged Del Bosque or his replacement to consider overhauling the national team.
"In football, the end of an era is usually signalled by a defeat. Maybe now's the time to start thinking about making changes," he said. "Things are going to change. Eras end with defeats -- and this was a painful defeat."