The Roja boss responded to reports that the new Chelsea midfielder was involved in an argument with the coach while he revealed he is unsure of Xavi's international future
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Spain's dispirited squad was once again in the headlines earlier on Sunday after rumours of an argument between Del Bosque and Fabregas over the new Chelsea signing's work-rate, with the coach appearing to take away the midfielder's bib.
However, the former Real Madrid boss insists he was simply balancing out teams in the training session and stressed he has to be concerned with keeping the entirety of his squad content - unlike the players themselves.
"I didn't take away the vest," Del Bosque said to Cuatro Television. "It was a minor issue. One team was outnumbered and the team were still behind. I sought support from Xabi Alonso. Nothing happened.
"I'm grateful to all the players. I think of them. But they only think of themselves."
Regarding his side's dreadful World Cup campaign, Del Bosque admits he is unable to put a finger on precisely what the key problems behind their performances were, but says he feels "hurt" by certain criticism within the Spanish media.
"I don’t want to look for excuses about the calendar being a factor against us," he said.
"It was a purely football matter, perhaps something concerning the physical or aspect or a question of tactics.
"Some of the criticism has hurt me because it has come from close to home. When I see on a Real Madrid webpage or a website related to Madrid that I am a puppet in the hands of the Barca players that hurts me.
"The rest I can accept. Those who are arguing that we haven't played well don't upset me. Even when we were winning we received criticism or my role has been questioned."
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"I can understand that you, the press, want to know what will happen but everything has a process. We have to make many considerations before any decisions are taken - for the good of Spanish football.
"We don't know whether he will continue or not. I sincerely don't know. Nobody has told me directly that these will be their last games with Spain."
Looking ahead to Spain's final game, against Australia, Del Bosque spoke of a desire to end a disappointing summer on a high note.
"We want to go out in the best way possible. I would have liked this game to come earlier; we've been waiting for it since the Holland game.
"Now, after three days, we have begun to understand the situation. We've all worked together and that has made it more manageable."