The Dutch went to Poland and Ukraine among the favourites to lift the trophy but failed to pick up a point in Group B, losing to Denmark, Germany and Portugal.
The future of coach Bert van Marwijk is now under scrutiny and his chances of staying in the role will not be helped by rumours of disharmony among the players.
Bayern Munich star Robben said: "Of course there were some internal issues but we will keep them indoors. But believe me we tried everything, it's just not worked.
"The hunger in the team is there but we failed together. And I mean the technical staff, the players, the whole team.
"This is the harsh reality of the sporting world. We must all, therefore, look in the mirror."
Captain Mark van Bommel, who was dropped for the clash with the Portuguese, admitted the atmosphere in the squad was different to that at the 2010 World Cup when Oranje made it to the final only to lose in extra-time to Spain.
The 35-year-old said: "I am captain and will always protect my players but the atmosphere was different than it was two years ago.
"Why that was I don't know, I can only speak for myself, not the other guys."
Holland had to win by two clear goals against Portugal and hope Denmark lost to Germany, and things looked bright when Rafael van der Vaart put them in front – but Ronaldo netted a brace for Paulo Bento's men.
Van der Vaart said: "I knew it would be difficult. We lost all confidence after losing the game against Denmark, and against Portugal we knew it could go wrong, and so it did. We have to start all over again."