Two first-half goals without reply saw Chile beat the title holders 2-0 and progress into the last-16 stage with a group game to spare.
Vicente del Bosque's side arrived in Brazil having won the last three major tournaments, and Alonso says that the team were not mentally equipped to deal with the pressure of vying for a fourth straight triumph.
"This is a great source of sadness," he told reporters. "Mentally we were not prepared for this competition, physically we arrived in the right condition.
"Putting everything together we were not in the best shape. We were not at a high level and were are deservedly out."
Spain conclude their campaign by facing Australia on Monday.