Taking part in the finals for the first time, Spain began their campaign in Canada with a 1-1 draw against Costa Rica but defeats by Brazil and South Korea left them with a single point from their three Group E games and without a place in the last 16.
"It's clear the preparation for the World Cup was inadequate," the 23-strong squad said in a statement on Friday.
"Non-existent warm-up games, a lack of acclimatisation, insufficient analysis of opponents and preparation of matches ... and that has been the pattern for a long time," they added.
"We believe an era has come to an end and we need a change. We have communicated that to the coach and the technical team."
Ranked 14th in the world, Spain's disappointing performance also meant they missed out on a place at next year's Olympic Games in Brazil.
As UEFA will not host a specific qualification tournament, the three best-placed European sides at the World Cup will secure a berth in Rio de Janeiro.
"On both an individual and group level the 23 players have been self-critical and we know we could have performed better," the squad said.
"This generation has the talent and commitment to have gone a great deal further."
(Reporting by Iain Rogers, editing by Tony Jimenez)
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