The European champions were aiming to bounce back from last weekend's 1-1 draw at home to Villarreal, but an excellent first-half header from Aritz Aduriz handed Bilbao a first win over Real since January 2010 in Saturday's contest at San Mames.
Real's attacking trio of Cristiano Ronaldo, Karim Benzema and Gareth Bale were frustrated in their attempts to force an equaliser and failed to hit their usually high standards.
Head coach Ancelotti, whose side will drop to second if Barcelona beat Rayo Vallecano on Sunday, admits Real have problems in attack, but refused to pin that on his players.
"The responsibility is mine," he told reporters. "Others may say it is the fault of the team. But this is my [responsibility].
"The team is playing badly and the league is complicated now. But it has not been completed and we will try to fix the problem quickly.
"Our problem is not with the defence it is offensively. We tried to find solutions, but in two games we have only scored a penalty. This is what we need to fix, we lack efficiency."
Asked whether there were any issues with Ronaldo, Benzema and Bale, he responded: "Not a single problem. They didn't have a good game but the blame doesn't just lie with those three.
"Everyone is responsible for our breakdown in attack."
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