Karim Benzema's second half goal secured a vital win for Los Blancos, and solidified their lead over Barcelona at the top of the La Liga table.
However the hosts struggled during the first half, as Diego Simeone's side caused problems for the Real Madrid defence, but Zidane insisted that he would shoulder the burden for poor performances.
"It was a complicated game against a good opponent," he told a post match interview with Diario AS.
"I am pleased with the win, but we had to improve in the second half. I take my share of responsibility for the first half, as we did not perform. I do not normally like to make changes at the break, but I felt I had to do something".