The holders became the first team to be eliminated in the group stage of this year’s tournament – and only the fifth defending champions to fall at this hurdle – following back-to-back defeats against Holland (5-1) and Chile (2-0).
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The Real Madrid defensive midfielder dismissed the rumours but refused to talk about his future with Spain, after reports suggested that the 32-year-old would retire following the tournament – a decision he supposedly made prior to the competition.
"I'm still not at that stage where I want to decide. What I want is, unfortunately, to finish this World Cup, go on vacation, disconnect a bit and then do one thing at a time," Alonso told Onda Cero.
"Right now I will not touch on that subject."
Although Vicente del Bosque’s side are already out of the World Cup, they will play one more game in Brazil when la Roja take on Australia on Monday.
Alonso insists that the atmosphere between the players is as good as it was two years ago - when the team won Euro 2012 - but believes that it was simply Spain’s lack of focus which ultimately led to their elimination from the World Cup.
"I will not say the things that happened in the locker room," he said.
"Our deficiencies depend on how you want to understand them. I think it is my perception but also that of many of my colleagues. We did not have the required voltage, or the competitive level against Holland and Chile.
"The co-existence between players from different clubs is the same as two years ago. Everything is much more natural, there are no such tensions that you might think. I hate talking about it."