La Roja set the unwelcome record of becoming the only champions to exit the event after just two matches of the group stage, losing 2-0 to Chile on Wednesday after being dismantled 5-1 by Netherlands.
Spain had previously dominated the global stage, claiming European Champions titles either side of their South Africa 2010 triumph.
Alonso said: "Things are going to change. Eras end with defeats... and this was a painful defeat.
"It's a completely unexpected failure but that is sport. These things happen. It was unexpected but we have to take the great sadnesses in the same way as we take the great joys, as men."
The 32-year-old conceded his team were lacking on various fronts.
"I believe that we haven't been able to maintain the same levels of conviction, of hunger. The success, the happiness of before is gone, it's run out and we haven't been able to keep it going.
"We've made lots of mistakes, we've lost a bit of our know-how, and we've paid for it with our solidity that had helped us win so many games.
"We've not been able to keep the same levels of ambition and hunger, perhaps the real conviction to go for the championship.
"I think it's a bit of everything. Mentally we weren't ready, physically maybe the same but, putting that all together, we weren't in the best shape.
"Then we have played against teams that were well-prepared and at their peak, and now we're going home.
"It hurts our pride a lot, but this is football. But as I said, we've known how to win and now we have to know how to lose."